diff --git a/bigquery/google/cloud/bigquery/table.py b/bigquery/google/cloud/bigquery/table.py
index ec0ea813615c1..742c1a3efad1e 100644
--- a/bigquery/google/cloud/bigquery/table.py
+++ b/bigquery/google/cloud/bigquery/table.py
@@ -1387,6 +1387,27 @@ def _to_dataframe_tabledata_list(self, dtypes, progress_bar=None):
 
         return pandas.concat(frames)
 
+    def _to_dataframe_bqstorage_stream(
+        self, bqstorage_client, dtypes, columns, session, stream
+    ):
+        position = bigquery_storage_v1beta1.types.StreamPosition(stream=stream)
+        rowstream = bqstorage_client.read_rows(position).rows(session)
+
+        frames = []
+        for page in rowstream.pages:
+            if self._to_dataframe_finished:
+                return
+            frames.append(page.to_dataframe(dtypes=dtypes))
+
+        # Avoid errors on unlucky streams with no blocks. pandas.concat
+        # will fail on an empty list.
+        if not frames:
+            return pandas.DataFrame(columns=columns)
+
+        # page.to_dataframe() does not preserve column order. Rearrange at
+        # the end using manually-parsed schema.
+        return pandas.concat(frames)[columns]
+
     def _to_dataframe_bqstorage(self, bqstorage_client, dtypes):
         """Use (faster, but billable) BQ Storage API to construct DataFrame."""
         if bigquery_storage_v1beta1 is None:
@@ -1422,28 +1443,9 @@ def _to_dataframe_bqstorage(self, bqstorage_client, dtypes):
         if not session.streams:
             return pandas.DataFrame(columns=columns)
 
-        # Use finished to notify worker threads when to quit. See:
-        # https://stackoverflow.com/a/29237343/101923
-        finished = False
-
-        def get_dataframe(stream):
-            position = bigquery_storage_v1beta1.types.StreamPosition(stream=stream)
-            rowstream = bqstorage_client.read_rows(position).rows(session)
-
-            frames = []
-            for page in rowstream.pages:
-                if finished:
-                    return
-                frames.append(page.to_dataframe(dtypes=dtypes))
-
-            # Avoid errors on unlucky streams with no blocks. pandas.concat
-            # will fail on an empty list.
-            if not frames:
-                return pandas.DataFrame(columns=columns)
-
-            # page.to_dataframe() does not preserve column order. Rearrange at
-            # the end using manually-parsed schema.
-            return pandas.concat(frames)[columns]
+        # Use _to_dataframe_finished to notify worker threads when to quit.
+        # See: https://stackoverflow.com/a/29237343/101923
+        self._to_dataframe_finished = False
 
         def get_frames(pool):
             frames = []
@@ -1451,8 +1453,17 @@ def get_frames(pool):
             # Manually submit jobs and wait for download to complete rather
             # than using pool.map because pool.map continues running in the
             # background even if there is an exception on the main thread.
+            # See: https://github.com/googleapis/google-cloud-python/pull/7698
             not_done = [
-                pool.submit(get_dataframe, stream) for stream in session.streams
+                pool.submit(
+                    self._to_dataframe_bqstorage_stream,
+                    bqstorage_client,
+                    dtypes,
+                    columns,
+                    session,
+                    stream,
+                )
+                for stream in session.streams
             ]
 
             while not_done:
@@ -1469,10 +1480,9 @@ def get_frames(pool):
                 # No need for a lock because reading/replacing a variable is
                 # defined to be an atomic operation in the Python language
                 # definition (enforced by the global interpreter lock).
-                finished = True
+                self._to_dataframe_finished = True
 
-        # Use [columns] to ensure column order matches manually-parsed schema.
-        return pandas.concat(frames)[columns]
+        return pandas.concat(frames)
 
     def _get_progress_bar(self, progress_bar_type):
         """Construct a tqdm progress bar object, if tqdm is installed."""