diff --git a/doc/source/whatsnew/v1.1.4.rst b/doc/source/whatsnew/v1.1.4.rst
index ee76fe9398002..81d781b51cb1f 100644
--- a/doc/source/whatsnew/v1.1.4.rst
+++ b/doc/source/whatsnew/v1.1.4.rst
@@ -21,6 +21,7 @@ Fixed regressions
 - Fixed regression in :meth:`Series.astype` converting ``None`` to ``"nan"`` when casting to string (:issue:`36904`)
 - Fixed regression in :class:`RollingGroupby` causing a segmentation fault with Index of dtype object (:issue:`36727`)
 - Fixed regression in :class:`PeriodDtype` comparing both equal and unequal to its string representation (:issue:`37265`)
+- Fixed regression where slicing :class:`DatetimeIndex` raised :exc:`AssertionError` on irregular time series with ``pd.NaT`` or on unsorted indices (:issue:`36953` and :issue:`35509`)
 - Fixed regression in certain offsets (:meth:`pd.offsets.Day() <pandas.tseries.offsets.Day>` and below) no longer being hashable (:issue:`37267`)
 - Fixed regression in :class:`StataReader` which required ``chunksize`` to be manually set when using an iterator to read a dataset (:issue:`37280`)
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index f5dbb77d16165..5d7f15be6e107 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -2880,6 +2880,8 @@ def __getitem__(self, key):
         # Do we have a slicer (on rows)?
         indexer = convert_to_index_sliceable(self, key)
         if indexer is not None:
+            if isinstance(indexer, np.ndarray):
+                indexer = lib.maybe_indices_to_slice(indexer, len(self))
             # either we have a slice or we have a string that can be converted
             #  to a slice for partial-string date indexing
             return self._slice(indexer, axis=0)
diff --git a/pandas/tests/indexing/test_partial.py b/pandas/tests/indexing/test_partial.py
index 337ec683ee745..15fb616528a21 100644
--- a/pandas/tests/indexing/test_partial.py
+++ b/pandas/tests/indexing/test_partial.py
@@ -681,3 +681,24 @@ def test_index_name_empty(self):
             {"series": [1.23] * 4}, index=pd.RangeIndex(4, name="series_index")
         )
         tm.assert_frame_equal(df, expected)
+
+    def test_slice_irregular_datetime_index_with_nan(self):
+        # GH36953
+        index = pd.to_datetime(["2012-01-01", "2012-01-02", "2012-01-03", None])
+        df = DataFrame(range(len(index)), index=index)
+        expected = DataFrame(range(len(index[:3])), index=index[:3])
+        result = df["2012-01-01":"2012-01-04"]
+        tm.assert_frame_equal(result, expected)
+
+    def test_slice_datetime_index(self):
+        # GH35509
+        df = DataFrame(
+            {"col1": ["a", "b", "c"], "col2": [1, 2, 3]},
+            index=pd.to_datetime(["2020-08-01", "2020-07-02", "2020-08-05"]),
+        )
+        expected = DataFrame(
+            {"col1": ["a", "c"], "col2": [1, 3]},
+            index=pd.to_datetime(["2020-08-01", "2020-08-05"]),
+        )
+        result = df.loc["2020-08"]
+        tm.assert_frame_equal(result, expected)