diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 3e22084d98234..21e45294c87a3 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -582,6 +582,7 @@ Datetimelike
 - Bug in :class:`DataFrame` comparisons against ``Timestamp``-like objects failing to raise ``TypeError`` for inequality checks with mismatched types (:issue:`8932`,:issue:`22163`)
 - Bug in :class:`DataFrame` with mixed dtypes including ``datetime64[ns]`` incorrectly raising ``TypeError`` on equality comparisons (:issue:`13128`,:issue:`22163`)
 - Bug in :meth:`DataFrame.eq` comparison against ``NaT`` incorrectly returning ``True`` or ``NaN`` (:issue:`15697`,:issue:`22163`)
+- Bug in :class:`DatetimeIndex` subtraction that incorrectly failed to raise `OverflowError` (:issue:`22492`, :issue:`22508`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 1dd34cdf73ab5..484eb430c82b1 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -459,7 +459,8 @@ def _sub_datelike_dti(self, other):
 
         self_i8 = self.asi8
         other_i8 = other.asi8
-        new_values = self_i8 - other_i8
+        new_values = checked_add_with_arr(self_i8, -other_i8,
+                                          arr_mask=self._isnan)
         if self.hasnans or other.hasnans:
             mask = (self._isnan) | (other._isnan)
             new_values[mask] = iNaT
diff --git a/pandas/tests/arithmetic/test_datetime64.py b/pandas/tests/arithmetic/test_datetime64.py
index 879a4e1b4af1a..d597ea834f097 100644
--- a/pandas/tests/arithmetic/test_datetime64.py
+++ b/pandas/tests/arithmetic/test_datetime64.py
@@ -1570,6 +1570,40 @@ def test_datetimeindex_sub_timestamp_overflow(self):
             with pytest.raises(OverflowError):
                 dtimin - variant
 
+    def test_datetimeindex_sub_datetimeindex_overflow(self):
+        # GH#22492, GH#22508
+        dtimax = pd.to_datetime(['now', pd.Timestamp.max])
+        dtimin = pd.to_datetime(['now', pd.Timestamp.min])
+
+        ts_neg = pd.to_datetime(['1950-01-01', '1950-01-01'])
+        ts_pos = pd.to_datetime(['1980-01-01', '1980-01-01'])
+
+        # General tests
+        expected = pd.Timestamp.max.value - ts_pos[1].value
+        result = dtimax - ts_pos
+        assert result[1].value == expected
+
+        expected = pd.Timestamp.min.value - ts_neg[1].value
+        result = dtimin - ts_neg
+        assert result[1].value == expected
+
+        with pytest.raises(OverflowError):
+            dtimax - ts_neg
+
+        with pytest.raises(OverflowError):
+            dtimin - ts_pos
+
+        # Edge cases
+        tmin = pd.to_datetime([pd.Timestamp.min])
+        t1 = tmin + pd.Timedelta.max + pd.Timedelta('1us')
+        with pytest.raises(OverflowError):
+            t1 - tmin
+
+        tmax = pd.to_datetime([pd.Timestamp.max])
+        t2 = tmax + pd.Timedelta.min - pd.Timedelta('1us')
+        with pytest.raises(OverflowError):
+            tmax - t2
+
     @pytest.mark.parametrize('names', [('foo', None, None),
                                        ('baz', 'bar', None),
                                        ('bar', 'bar', 'bar')])