diff --git a/django/db/backends/__init__.py b/django/db/backends/__init__.py
index 0f9423c1c3e..2a7a206c3b8 100644
--- a/django/db/backends/__init__.py
+++ b/django/db/backends/__init__.py
@@ -352,6 +352,18 @@ class BaseDatabaseWrapper(object):
     def make_debug_cursor(self, cursor):
         return util.CursorDebugWrapper(cursor, self)
 
+    @contextmanager
+    def temporary_connection(self):
+        # Ensure a connection is established, and avoid leaving a dangling
+        # connection, for operations outside of the request-response cycle.
+        must_close = self.connection is None
+        cursor = self.cursor()
+        try:
+            yield
+        finally:
+            cursor.close()
+            if must_close:
+                self.close()
 
 class BaseDatabaseFeatures(object):
     allows_group_by_pk = False
diff --git a/django/db/backends/mysql/base.py b/django/db/backends/mysql/base.py
index 3719b3a6a79..fc2ff315813 100644
--- a/django/db/backends/mysql/base.py
+++ b/django/db/backends/mysql/base.py
@@ -453,7 +453,8 @@ class DatabaseWrapper(BaseDatabaseWrapper):
 
     @cached_property
     def mysql_version(self):
-        server_info = self.connection.get_server_info()
+        with self.temporary_connection():
+            server_info = self.connection.get_server_info()
         match = server_version_re.match(server_info)
         if not match:
             raise Exception('Unable to determine MySQL version from version string %r' % server_info)
diff --git a/django/db/backends/oracle/base.py b/django/db/backends/oracle/base.py
index 3fdf67402a9..a9ae0251467 100644
--- a/django/db/backends/oracle/base.py
+++ b/django/db/backends/oracle/base.py
@@ -623,8 +623,10 @@ class DatabaseWrapper(BaseDatabaseWrapper):
 
     @cached_property
     def oracle_version(self):
+        with self.temporary_connection():
+            version = self.connection.version
         try:
-            return int(self.connection.version.split('.')[0])
+            return int(version.split('.')[0])
         except ValueError:
             return None
 
diff --git a/django/db/backends/postgresql_psycopg2/base.py b/django/db/backends/postgresql_psycopg2/base.py
index 831ad84843f..85a0991402c 100644
--- a/django/db/backends/postgresql_psycopg2/base.py
+++ b/django/db/backends/postgresql_psycopg2/base.py
@@ -152,7 +152,8 @@ class DatabaseWrapper(BaseDatabaseWrapper):
 
     @cached_property
     def pg_version(self):
-        return get_version(self.connection)
+        with self.temporary_connection():
+            return get_version(self.connection)
 
     def get_connection_params(self):
         settings_dict = self.settings_dict
diff --git a/django/db/backends/postgresql_psycopg2/operations.py b/django/db/backends/postgresql_psycopg2/operations.py
index 8e87ed539f1..56535e08650 100644
--- a/django/db/backends/postgresql_psycopg2/operations.py
+++ b/django/db/backends/postgresql_psycopg2/operations.py
@@ -195,8 +195,7 @@ class DatabaseOperations(BaseDatabaseOperations):
         NotImplementedError if this is the database in use.
         """
         if aggregate.sql_function in ('STDDEV_POP', 'VAR_POP'):
-            pg_version = self.connection.pg_version
-            if pg_version >= 80200 and pg_version <= 80204:
+            if 80200 <= self.connection.pg_version <= 80204:
                 raise NotImplementedError('PostgreSQL 8.2 to 8.2.4 is known to have a faulty implementation of %s. Please upgrade your version of PostgreSQL.' % aggregate.sql_function)
 
     def max_name_length(self):