diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index cea42cbffa906..68b13c2fe28f5 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -712,6 +712,7 @@ Reshaping
 - Fixed regression in :func:`merge` on merging DatetimeIndex with empty DataFrame (:issue:`36895`)
 - Bug in :meth:`DataFrame.apply` not setting index of return value when ``func`` return type is ``dict`` (:issue:`37544`)
 - Bug in :func:`concat` resulting in a ``ValueError`` when at least one of both inputs had a non-unique index (:issue:`36263`)
+- Bug in :meth:`DataFrame.merge` and :meth:`pandas.merge` returning inconsistent ordering in result for ``how=right`` and ``how=left`` (:issue:`35382`)
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 918a894a27916..cdcd6b19704c4 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -1358,12 +1358,14 @@ def get_join_indexers(
     lkey, rkey, count = _factorize_keys(lkey, rkey, sort=sort, how=how)
     # preserve left frame order if how == 'left' and sort == False
     kwargs = copy.copy(kwargs)
-    if how == "left":
+    if how in ("left", "right"):
         kwargs["sort"] = sort
     join_func = {
         "inner": libjoin.inner_join,
         "left": libjoin.left_outer_join,
-        "right": _right_outer_join,
+        "right": lambda x, y, count, **kwargs: libjoin.left_outer_join(
+            y, x, count, **kwargs
+        )[::-1],
         "outer": libjoin.full_outer_join,
     }[how]
 
@@ -1883,11 +1885,6 @@ def _left_join_on_index(left_ax: Index, right_ax: Index, join_keys, sort: bool =
     return left_ax, None, right_indexer
 
 
-def _right_outer_join(x, y, max_groups):
-    right_indexer, left_indexer = libjoin.left_outer_join(y, x, max_groups)
-    return left_indexer, right_indexer
-
-
 def _factorize_keys(
     lk: ArrayLike, rk: ArrayLike, sort: bool = True, how: str = "inner"
 ) -> Tuple[np.ndarray, np.ndarray, int]:
diff --git a/pandas/tests/reshape/merge/test_merge.py b/pandas/tests/reshape/merge/test_merge.py
index 999b827fe0571..9ccfdfc146eac 100644
--- a/pandas/tests/reshape/merge/test_merge.py
+++ b/pandas/tests/reshape/merge/test_merge.py
@@ -601,6 +601,18 @@ def test_merge_nosort(self):
 
         assert (df.var3.unique() == result.var3.unique()).all()
 
+    @pytest.mark.parametrize(
+        ("sort", "values"), [(False, [1, 1, 0, 1, 1]), (True, [0, 1, 1, 1, 1])]
+    )
+    @pytest.mark.parametrize("how", ["left", "right"])
+    def test_merge_same_order_left_right(self, sort, values, how):
+        # GH#35382
+        df = DataFrame({"a": [1, 0, 1]})
+
+        result = df.merge(df, on="a", how=how, sort=sort)
+        expected = DataFrame(values, columns=["a"])
+        tm.assert_frame_equal(result, expected)
+
     def test_merge_nan_right(self):
         df1 = DataFrame({"i1": [0, 1], "i2": [0, 1]})
         df2 = DataFrame({"i1": [0], "i3": [0]})