diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 9947866a76e3f..81e1d84880f60 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -278,6 +278,9 @@ def apply_standard(self):
         if (
             self.result_type in ["reduce", None]
             and not self.dtypes.apply(is_extension_array_dtype).any()
+            # Disallow dtypes where setting _index_data will break
+            #  ExtensionArray values, see GH#31182
+            and not self.dtypes.apply(lambda x: x.kind in ["m", "M"]).any()
             # Disallow complex_internals since libreduction shortcut raises a TypeError
             and not self.agg_axis._has_complex_internals
         ):
diff --git a/pandas/core/base.py b/pandas/core/base.py
index 6ad237cbc7c51..05e3302abddbe 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -1265,6 +1265,10 @@ def unique(self):
         if hasattr(values, "unique"):
 
             result = values.unique()
+            if self.dtype.kind in ["m", "M"] and isinstance(self, ABCSeries):
+                # GH#31182 Series._values returns EA, unpack for backward-compat
+                if getattr(self.dtype, "tz", None) is None:
+                    result = np.asarray(result)
         else:
             result = unique1d(values)
 
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index d29954c677c5d..22901051ec345 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2151,6 +2151,10 @@ def get_values(self, dtype=None):
             return result.reshape(self.values.shape)
         return self.values
 
+    def internal_values(self):
+        # Override to return DatetimeArray and TimedeltaArray
+        return self.array_values()
+
 
 class DatetimeBlock(DatetimeLikeBlockMixin, Block):
     __slots__ = ()
@@ -2284,6 +2288,7 @@ class DatetimeTZBlock(ExtensionBlock, DatetimeBlock):
     is_datetimetz = True
     is_extension = True
 
+    internal_values = Block.internal_values
     _can_hold_element = DatetimeBlock._can_hold_element
     to_native_types = DatetimeBlock.to_native_types
     fill_value = np.datetime64("NaT", "ns")
diff --git a/pandas/core/series.py b/pandas/core/series.py
index e9df0938d5f98..0aaa583885bc3 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -493,7 +493,8 @@ def _values(self):
         """
         Return the internal repr of this data (defined by Block.interval_values).
         This are the values as stored in the Block (ndarray or ExtensionArray
-        depending on the Block class).
+        depending on the Block class), with datetime64[ns] and timedelta64[ns]
+        wrapped in ExtensionArrays to match Index._values behavior.
 
         Differs from the public ``.values`` for certain data types, because of
         historical backwards compatibility of the public attribute (e.g. period
@@ -502,8 +503,9 @@ def _values(self):
         cases).
 
         Differs from ``.array`` in that this still returns the numpy array if
-        the Block is backed by a numpy array, while ``.array`` ensures to always
-        return an ExtensionArray.
+        the Block is backed by a numpy array (except for datetime64 and
+        timedelta64 dtypes), while ``.array`` ensures to always return an
+        ExtensionArray.
 
         Differs from ``._ndarray_values``, as that ensures to always return a
         numpy array (it will call ``_ndarray_values`` on the ExtensionArray, if
@@ -515,8 +517,9 @@ def _values(self):
         ----------- | ------------- | ------------- | ------------- | --------------- |
         Numeric     | ndarray       | ndarray       | PandasArray   | ndarray         |
         Category    | Categorical   | Categorical   | Categorical   | ndarray[int]    |
-        dt64[ns]    | ndarray[M8ns] | ndarray[M8ns] | DatetimeArray | ndarray[M8ns]   |
+        dt64[ns]    | ndarray[M8ns] | DatetimeArray | DatetimeArray | ndarray[M8ns]   |
         dt64[ns tz] | ndarray[M8ns] | DatetimeArray | DatetimeArray | ndarray[M8ns]   |
+        td64[ns]    | ndarray[m8ns] | TimedeltaArray| ndarray[m8ns] | ndarray[m8ns]   |
         Period      | ndarray[obj]  | PeriodArray   | PeriodArray   | ndarray[int]    |
         Nullable    | EA            | EA            | EA            | ndarray         |
 
diff --git a/pandas/tests/indexes/datetimes/test_tools.py b/pandas/tests/indexes/datetimes/test_tools.py
index a5332eaea0432..7abf810e6bcfc 100644
--- a/pandas/tests/indexes/datetimes/test_tools.py
+++ b/pandas/tests/indexes/datetimes/test_tools.py
@@ -1583,7 +1583,7 @@ def test_string_na_nat_conversion(self, cache):
         for i in range(5):
             x = series[i]
             if isna(x):
-                expected[i] = iNaT
+                expected[i] = pd.NaT
             else:
                 expected[i] = to_datetime(x, cache=cache)
 
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 7400b049961d5..8d2058ffab643 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -316,7 +316,12 @@ def test_invalid_td64_reductions(self, opname):
         )
         td = s.diff()
 
-        msg = "reduction operation '{op}' not allowed for this dtype"
+        msg = "|".join(
+            [
+                "reduction operation '{op}' not allowed for this dtype",
+                r"cannot perform {op} with type timedelta64\[ns\]",
+            ]
+        )
         msg = msg.format(op=opname)
 
         with pytest.raises(TypeError, match=msg):
@@ -648,7 +653,13 @@ def test_ops_consistency_on_empty(self, method):
         # timedelta64[ns]
         tdser = Series([], dtype="m8[ns]")
         if method == "var":
-            with pytest.raises(TypeError, match="operation 'var' not allowed"):
+            msg = "|".join(
+                [
+                    "operation 'var' not allowed",
+                    r"cannot perform var with type timedelta64\[ns\]",
+                ]
+            )
+            with pytest.raises(TypeError, match=msg):
                 getattr(tdser, method)()
         else:
             result = getattr(tdser, method)()