diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index c9267a756bef3..f3d4d53b00aa2 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -786,6 +786,7 @@ Reshaping
 ^^^^^^^^^
 - Bug in :func:`merge` raising error when performing an inner join with partial index and ``right_index`` when no overlap between indices (:issue:`33814`)
 - Bug in :meth:`DataFrame.unstack` with missing levels led to incorrect index names (:issue:`37510`)
+- Bug in :func:`merge_asof` propagating the right Index with ``left_index=True`` and ``right_on`` specification instead of left Index (:issue:`33463`)
 - Bug in :func:`join` over :class:`MultiIndex` returned wrong result, when one of both indexes had only one level (:issue:`36909`)
 - :meth:`merge_asof` raises ``ValueError`` instead of cryptic ``TypeError`` in case of non-numerical merge columns (:issue:`29130`)
 - Bug in :meth:`DataFrame.join` not assigning values correctly when having :class:`MultiIndex` where at least one dimension is from dtype ``Categorical`` with non-alphabetically sorted categories (:issue:`38502`)
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 94d78f6b54b91..8cee0dd2abb88 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -969,7 +969,16 @@ def _get_join_info(
                     join_index = self.right.index.take(right_indexer)
                     left_indexer = np.array([-1] * len(join_index), dtype=np.intp)
             elif self.left_index:
-                if len(self.right) > 0:
+                if self.how == "asof":
+                    # GH#33463 asof should always behave like a left merge
+                    join_index = self._create_join_index(
+                        self.left.index,
+                        self.right.index,
+                        left_indexer,
+                        how="left",
+                    )
+
+                elif len(self.right) > 0:
                     join_index = self._create_join_index(
                         self.right.index,
                         self.left.index,
diff --git a/pandas/tests/reshape/merge/test_merge_asof.py b/pandas/tests/reshape/merge/test_merge_asof.py
index 3f5bb9b84372c..671f0ad2d26c7 100644
--- a/pandas/tests/reshape/merge/test_merge_asof.py
+++ b/pandas/tests/reshape/merge/test_merge_asof.py
@@ -6,6 +6,7 @@
 
 import pandas as pd
 from pandas import (
+    Index,
     Timedelta,
     merge_asof,
     read_csv,
@@ -1338,7 +1339,9 @@ def test_merge_index_column_tz(self):
                 "from_date": index[1:],
                 "abc": [2.46] * 3 + [2.19],
             },
-            index=pd.Index([1, 2, 3, 4]),
+            index=pd.date_range(
+                "2019-10-01 00:30:00", freq="30min", periods=4, tz="UTC"
+            ),
         )
         tm.assert_frame_equal(result, expected)
 
@@ -1351,7 +1354,7 @@ def test_merge_index_column_tz(self):
                 "abc": [2.46] * 4 + [2.19],
                 "xyz": [np.nan, 0.9, 0.8, 0.7, 0.6],
             },
-            index=pd.Index([0, 1, 2, 3, 4]),
+            index=Index([0, 1, 2, 3, 4]),
         )
         tm.assert_frame_equal(result, expected)
 
@@ -1412,3 +1415,25 @@ def test_merge_asof_non_numerical_dtype_object():
             left_by="a",
             right_by="left_val",
         )
+
+
+@pytest.mark.parametrize(
+    "kwargs",
+    [
+        {"right_index": True, "left_index": True},
+        {"left_on": "left_time", "right_index": True},
+        {"left_index": True, "right_on": "right"},
+    ],
+)
+def test_merge_asof_index_behavior(kwargs):
+    # GH 33463
+    index = Index([1, 5, 10], name="test")
+    left = pd.DataFrame({"left": ["a", "b", "c"], "left_time": [1, 4, 10]}, index=index)
+    right = pd.DataFrame({"right": [1, 2, 3, 6, 7]}, index=[1, 2, 3, 6, 7])
+    result = merge_asof(left, right, **kwargs)
+
+    expected = pd.DataFrame(
+        {"left": ["a", "b", "c"], "left_time": [1, 4, 10], "right": [1, 3, 7]},
+        index=index,
+    )
+    tm.assert_frame_equal(result, expected)