diff --git a/Lib/concurrent/futures/_base.py b/Lib/concurrent/futures/_base.py
@@ -304,18 +304,6 @@ def wait(fs, timeout=None, return_when=ALL_COMPLETED):
     done.update(waiter.finished_futures)
     return DoneAndNotDoneFutures(done, fs - done)
 
-
-def _result_or_cancel(fut, timeout=None):
-    try:
-        try:
-            return fut.result(timeout)
-        finally:
-            fut.cancel()
-    finally:
-        # Break a reference cycle with the exception in self._exception
-        del fut
-
-
 class Future(object):
     """Represents the result of an asynchronous computation."""
 
@@ -625,23 +613,35 @@ def map(self, fn, *iterables, timeout=None, chunksize=1, buffersize=None):
         # before the first iterator value is required.
         def result_iterator():
             try:
-                # reverse to keep finishing order
+                # reverse so that the next (FIFO) future is on the right
                 fs.reverse()
+                # careful not to keep references to futures or results
                 while fs:
+                    # wait for the next result
+                    if timeout is None:
+                        fs[-1].result()
+                    else:
+                        fs[-1].result(end_time - time.monotonic())
+
+                    # buffer next task
                     if (
                         buffersize
                         and (executor := executor_weakref())
                         and (args := next(zipped_iterables, None))
                     ):
                         fs.appendleft(executor.submit(fn, *args))
-                    # Careful not to keep a reference to the popped future
-                    if timeout is None:
-                        yield _result_or_cancel(fs.pop())
-                    else:
-                        yield _result_or_cancel(fs.pop(), end_time - time.monotonic())
+
+                    # yield the awaited result
+                    yield fs.pop()._result
+
             finally:
+                # break the reference cycle with fs[-1]._exception's traceback
+                if fs:
+                    fs.pop().cancel()
+
                 for future in fs:
                     future.cancel()
+
         return result_iterator()
 
     def shutdown(self, wait=True, *, cancel_futures=False):

diff --git a/Lib/test/test_concurrent_futures/executor.py b/Lib/test/test_concurrent_futures/executor.py
@@ -3,7 +3,9 @@
 import time
 import weakref
 from concurrent import futures
-from operator import add
+from contextlib import suppress
+from functools import partial
+from operator import add, truediv
 from test import support
 from test.support import Py_GIL_DISABLED
 
@@ -143,6 +145,29 @@ def test_map_buffersize_when_buffer_is_full(self):
             msg="should have fetched only `buffersize` elements from `ints`.",
         )
 
+    def test_map_buffersize_when_error(self):
+        ints = [1, 2, 3, 0, 4, 5, 6]
+        index_of_zero = ints.index(0)
+        ints_iter = iter(ints)
+        buffersize = 2
+        reciprocal = partial(truediv, 1)
+        results = []
+        with suppress(ZeroDivisionError):
+            for result in self.executor.map(
+                reciprocal, ints_iter, buffersize=buffersize
+            ):
+                results.append(result)
+        self.assertEqual(
+            len(results),
+            index_of_zero,
+            msg="should have mapped until reaching the zero.",
+        )
+        self.assertEqual(
+            len(results) + buffersize + len(list(ints_iter)),
+            len(ints),
+            msg="ints should be either processed, or buffered, or not fetched.",
+        )
+
     def test_shutdown_race_issue12456(self):
         # Issue #12456: race condition at shutdown where trying to post a
         # sentinel in the call queue blocks (the queue is full while processes