diff --git a/pymongo/bulk.py b/pymongo/bulk.py
index c056e80fd..5bc468096 100644
--- a/pymongo/bulk.py
+++ b/pymongo/bulk.py
@@ -240,8 +240,9 @@ class _Bulk(object):
         listeners = client._event_listeners
 
         with self.collection.database.client._tmp_session(session) as s:
-            # sock_info.command checks auth, but we use sock_info.write_command.
-            sock_info.check_session_auth_matches(s)
+            # sock_info.command validates the session, but we use
+            # sock_info.write_command.
+            sock_info.validate_session(client, s)
             for run in generator:
                 cmd = SON([(_COMMANDS[run.op_type], self.collection.name),
                            ('ordered', self.ordered)])
@@ -267,10 +268,7 @@ class _Bulk(object):
                     if not to_send:
                         raise InvalidOperation("cannot do an empty bulk write")
                     result = bwc.write_command(request_id, msg, to_send)
-                    client._receive_cluster_time(result)
-                    if s is not None:
-                        s._advance_cluster_time(result.get("$clusterTime"))
-                        s._advance_operation_time(result.get("operationTime"))
+                    client._receive_cluster_time(result, s)
                     results.append((idx_offset, result))
                     if self.ordered and "writeErrors" in result:
                         break
diff --git a/pymongo/client_session.py b/pymongo/client_session.py
index 151b701e3..841a79f60 100644
--- a/pymongo/client_session.py
+++ b/pymongo/client_session.py
@@ -91,7 +91,7 @@ class ClientSession(object):
 
     def _end_session(self, lock):
         if self._server_session is not None:
-            self.client._return_server_session(self._server_session, lock)
+            self._client._return_server_session(self._server_session, lock)
             self._server_session = None
 
     def __enter__(self):
diff --git a/pymongo/command_cursor.py b/pymongo/command_cursor.py
index 72ec2be6a..ba5ba9478 100644
--- a/pymongo/command_cursor.py
+++ b/pymongo/command_cursor.py
@@ -154,12 +154,7 @@ class CommandCursor(object):
                                          self.__collection.codec_options)
             if from_command:
                 first = docs[0]
-                client._receive_cluster_time(first)
-                if self.__session is not None:
-                    self.__session._advance_cluster_time(
-                        first.get('$clusterTime'))
-                    self.__session._advance_operation_time(
-                        first.get('operationTime'))
+                client._receive_cluster_time(first, self.__session)
                 helpers._check_command_response(first)
 
         except OperationFailure as exc:
diff --git a/pymongo/cursor.py b/pymongo/cursor.py
index bddd3497c..2c50e3d8b 100644
--- a/pymongo/cursor.py
+++ b/pymongo/cursor.py
@@ -968,12 +968,7 @@ class Cursor(object):
                                          codec_options=self.__codec_options)
             if from_command:
                 first = docs[0]
-                client._receive_cluster_time(first)
-                if self.__session is not None:
-                    self.__session._advance_cluster_time(
-                        first.get("$clusterTime"))
-                    self.__session._advance_operation_time(
-                        first.get("operationTime"))
+                client._receive_cluster_time(first, self.__session)
                 helpers._check_command_response(first)
         except OperationFailure as exc:
             self.__killed = True
diff --git a/pymongo/message.py b/pymongo/message.py
index cc18472c7..8773b8da5 100644
--- a/pymongo/message.py
+++ b/pymongo/message.py
@@ -295,7 +295,7 @@ class _Query(object):
                 'Specifying a collation is unsupported with a max wire '
                 'version of %d.' % (sock_info.max_wire_version,))
 
-        sock_info.check_session_auth_matches(self.session)
+        sock_info.validate_session(self.client, self.session)
 
         return use_find_cmd
 
@@ -369,7 +369,7 @@ class _GetMore(object):
         self.max_await_time_ms = max_await_time_ms
 
     def use_command(self, sock_info, exhaust):
-        sock_info.check_session_auth_matches(self.session)
+        sock_info.validate_session(self.client, self.session)
         return sock_info.max_wire_version >= 4 and not exhaust
 
     def as_command(self):
diff --git a/pymongo/mongo_client.py b/pymongo/mongo_client.py
index f8764026f..f2a24e2f6 100644
--- a/pymongo/mongo_client.py
+++ b/pymongo/mongo_client.py
@@ -1356,8 +1356,12 @@ class MongoClient(common.BaseObject):
         if cluster_time:
             command['$clusterTime'] = cluster_time
 
-    def _receive_cluster_time(self, reply):
-        self._topology.receive_cluster_time(reply.get('$clusterTime'))
+    def _receive_cluster_time(self, reply, session):
+        cluster_time = reply.get('$clusterTime')
+        self._topology.receive_cluster_time(cluster_time)
+        if session is not None:
+            session._advance_cluster_time(cluster_time)
+            session._advance_operation_time(reply.get("operationTime"))
 
     def server_info(self, session=None):
         """Get information about the MongoDB server we're connected to.
diff --git a/pymongo/network.py b/pymongo/network.py
index 09a77b020..8d76412dc 100644
--- a/pymongo/network.py
+++ b/pymongo/network.py
@@ -129,12 +129,7 @@ def command(sock, dbname, spec, slave_ok, is_mongos,
 
         response_doc = unpacked_docs[0]
         if client:
-            client._receive_cluster_time(response_doc)
-            if session:
-                session._advance_cluster_time(
-                    response_doc.get('$clusterTime'))
-                session._advance_operation_time(
-                    response_doc.get('operationTime'))
+            client._receive_cluster_time(response_doc, session)
         if check:
             helpers._check_command_response(
                 response_doc, None, allowable_errors,
diff --git a/pymongo/pool.py b/pymongo/pool.py
index 2a340a2ed..289d72e5c 100644
--- a/pymongo/pool.py
+++ b/pymongo/pool.py
@@ -461,7 +461,7 @@ class SocketInfo(object):
           - `client`: optional MongoClient for gossipping $clusterTime.
           - `retryable_write`: True if this command is a retryable write.
         """
-        self.check_session_auth_matches(session)
+        self.validate_session(client, session)
         if (read_concern and self.max_wire_version < 4
                 and not read_concern.ok_for_legacy):
             raise ConfigurationError(
@@ -591,11 +591,21 @@ class SocketInfo(object):
         auth.authenticate(credentials, self)
         self.authset.add(credentials)
 
-    def check_session_auth_matches(self, session):
-        """Raise error if a ClientSession is logged in as a different user."""
-        if session and session._authset != self.authset:
-            raise InvalidOperation('session was used after authenticating'
-                                   ' with different credentials')
+    def validate_session(self, client, session):
+        """Validate this session before use with client.
+
+        Raises error if this session is logged in as a different user or
+        the client is not the one that created the session.
+        """
+        if session:
+            if session._client is not client:
+                raise InvalidOperation(
+                    'Can only use session with the MongoClient that'
+                    ' started it')
+            if session._authset != self.authset:
+                raise InvalidOperation(
+                    'Cannot use session after authenticating with different'
+                    ' credentials')
 
     def close(self):
         self.closed = True
diff --git a/test/test_session.py b/test/test_session.py
index 597ac6b4f..15816b3f2 100644
--- a/test/test_session.py
+++ b/test/test_session.py
@@ -57,19 +57,25 @@ def session_ids(client):
 
 
 class TestSession(IntegrationTest):
+
+    @classmethod
     @client_context.require_sessions
-    def setUp(self):
-        super(TestSession, self).setUp()
+    def setUpClass(cls):
+        super(TestSession, cls).setUpClass()
+        # Create a second client so we can make sure clients cannot share
+        # sessions.
+        cls.client2 = rs_or_single_client()
 
         # Redact no commands, so we can test user-admin commands have "lsid".
-        self.sensitive_commands = monitoring._SENSITIVE_COMMANDS.copy()
+        cls.sensitive_commands = monitoring._SENSITIVE_COMMANDS.copy()
         monitoring._SENSITIVE_COMMANDS.clear()
 
-    def tearDown(self):
-        monitoring._SENSITIVE_COMMANDS.update(self.sensitive_commands)
-        super(TestSession, self).tearDown()
+    @classmethod
+    def tearDownClass(cls):
+        monitoring._SENSITIVE_COMMANDS.update(cls.sensitive_commands)
+        super(TestSession, cls).tearDownClass()
 
-    def _test_ops(self, client, *ops, **kwargs):
+    def _test_ops(self, client, *ops):
         listener = client.event_listeners()[0][0]
 
         for f, args, kw in ops:
@@ -103,6 +109,18 @@ class TestSession(IntegrationTest):
             with self.assertRaisesRegex(InvalidOperation, "ended session"):
                 f(*args, **kw)
 
+            # Test a session cannot be used on another client.
+            with self.client2.start_session() as s:
+                # In case "f" modifies its inputs.
+                args = copy.copy(args)
+                kw = copy.copy(kw)
+                kw['session'] = s
+                with self.assertRaisesRegex(
+                        InvalidOperation,
+                        'Can only use session with the MongoClient'
+                        ' that started it'):
+                    f(*args, **kw)
+
         # No explicit session.
         for f, args, kw in ops:
             listener.results.clear()
@@ -980,8 +998,8 @@ class TestSessionsMultiAuth(IntegrationTest):
             client.admin.logout()
             db.authenticate('second-user', 'pass')
 
-            err = 'session was used after authenticating with different' \
-                  ' credentials'
+            err = ('Cannot use session after authenticating with different'
+                   ' credentials')
 
             with self.assertRaisesRegex(InvalidOperation, err):
                 # Auth has changed between find and getMore.