diff --git a/doc/source/whatsnew/v0.23.1.txt b/doc/source/whatsnew/v0.23.1.txt
index 4876678baaa6e..f400de5f1ad02 100644
--- a/doc/source/whatsnew/v0.23.1.txt
+++ b/doc/source/whatsnew/v0.23.1.txt
@@ -52,6 +52,7 @@ Groupby/Resample/Rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 
 - Bug in :func:`DataFrame.agg` where applying multiple aggregation functions to a :class:`DataFrame` with duplicated column names would cause a stack overflow (:issue:`21063`)
+- Bug in :func:`pandas.core.groupby.GroupBy.ffill` and :func:`pandas.core.groupby.GroupBy.bfill` where the fill within a grouping would not always be applied as intended due to the implementations' use of a non-stable sort (:issue:`21207`)
 
 Strings
 ^^^^^^^
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index 43afd1e0f5969..a6dbaff17e543 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -297,7 +297,8 @@ def group_fillna_indexer(ndarray[int64_t] out, ndarray[int64_t] labels,
     # Make sure all arrays are the same size
     assert N == len(labels) == len(mask)
 
-    sorted_labels = np.argsort(labels).astype(np.int64, copy=False)
+    sorted_labels = np.argsort(labels, kind='mergesort').astype(
+        np.int64, copy=False)
     if direction == 'bfill':
         sorted_labels = sorted_labels[::-1]
 
diff --git a/pandas/tests/groupby/test_transform.py b/pandas/tests/groupby/test_transform.py
index 626057c1ea760..7fccf1f57a886 100644
--- a/pandas/tests/groupby/test_transform.py
+++ b/pandas/tests/groupby/test_transform.py
@@ -721,6 +721,23 @@ def interweave(list_obj):
         assert_frame_equal(result, exp)
 
 
+@pytest.mark.parametrize("fill_method", ['ffill', 'bfill'])
+def test_pad_stable_sorting(fill_method):
+    # GH 21207
+    x = [0] * 20
+    y = [np.nan] * 10 + [1] * 10
+
+    if fill_method == 'bfill':
+        y = y[::-1]
+
+    df = pd.DataFrame({'x': x, 'y': y})
+    expected = df.copy()
+
+    result = getattr(df.groupby('x'), fill_method)()
+
+    tm.assert_frame_equal(result, expected)
+
+
 @pytest.mark.parametrize("test_series", [True, False])
 @pytest.mark.parametrize("periods,fill_method,limit", [
     (1, 'ffill', None), (1, 'ffill', 1),