diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index f86b307e5ede3..2206fd3316685 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -473,6 +473,8 @@ def __setitem__(
         # to a period in from_sequence). For DatetimeArray, it's Timestamp...
         # I don't know if mypy can do that, possibly with Generics.
         # https://mypy.readthedocs.io/en/latest/generics.html
+        if lib.is_scalar(value) and not isna(value):
+            value = com.maybe_box_datetimelike(value)
 
         if is_list_like(value):
             is_slice = isinstance(key, slice)
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 6d70fcfb62d52..563faab98d68b 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2230,7 +2230,9 @@ def _can_hold_element(self, element):
         if tipo is not None:
             if self.is_datetimetz:
                 # require exact match, since non-nano does not exist
-                return is_dtype_equal(tipo, self.dtype)
+                return is_dtype_equal(tipo, self.dtype) or is_valid_nat_for_dtype(
+                    element, self.dtype
+                )
 
             # GH#27419 if we get a non-nano datetime64 object
             return is_datetime64_dtype(tipo)
@@ -2500,26 +2502,28 @@ def concat_same_type(self, to_concat, placement=None):
     def fillna(self, value, limit=None, inplace=False, downcast=None):
         # We support filling a DatetimeTZ with a `value` whose timezone
         # is different by coercing to object.
-        try:
+        if self._can_hold_element(value):
             return super().fillna(value, limit, inplace, downcast)
-        except (ValueError, TypeError):
-            # different timezones, or a non-tz
-            return self.astype(object).fillna(
-                value, limit=limit, inplace=inplace, downcast=downcast
-            )
+
+        # different timezones, or a non-tz
+        return self.astype(object).fillna(
+            value, limit=limit, inplace=inplace, downcast=downcast
+        )
 
     def setitem(self, indexer, value):
         # https://github.com/pandas-dev/pandas/issues/24020
         # Need a dedicated setitem until #24020 (type promotion in setitem
         # for extension arrays) is designed and implemented.
-        try:
+        if self._can_hold_element(value) or (
+            isinstance(indexer, np.ndarray) and indexer.size == 0
+        ):
             return super().setitem(indexer, value)
-        except (ValueError, TypeError):
-            obj_vals = self.values.astype(object)
-            newb = make_block(
-                obj_vals, placement=self.mgr_locs, klass=ObjectBlock, ndim=self.ndim
-            )
-            return newb.setitem(indexer, value)
+
+        obj_vals = self.values.astype(object)
+        newb = make_block(
+            obj_vals, placement=self.mgr_locs, klass=ObjectBlock, ndim=self.ndim
+        )
+        return newb.setitem(indexer, value)
 
     def equals(self, other):
         # override for significant performance improvement
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index 58c2f3fc65bb2..d749d9bb47d25 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -179,6 +179,22 @@ def test_setitem_clears_freq(self):
         a[0] = pd.Timestamp("2000", tz="US/Central")
         assert a.freq is None
 
+    @pytest.mark.parametrize(
+        "obj",
+        [
+            pd.Timestamp.now(),
+            pd.Timestamp.now().to_datetime64(),
+            pd.Timestamp.now().to_pydatetime(),
+        ],
+    )
+    def test_setitem_objects(self, obj):
+        # make sure we accept datetime64 and datetime in addition to Timestamp
+        dti = pd.date_range("2000", periods=2, freq="D")
+        arr = dti._data
+
+        arr[0] = obj
+        assert arr[0] == obj
+
     def test_repeat_preserves_tz(self):
         dti = pd.date_range("2000", periods=2, freq="D", tz="US/Central")
         arr = DatetimeArray(dti)
diff --git a/pandas/tests/arrays/test_timedeltas.py b/pandas/tests/arrays/test_timedeltas.py
index 5825f9f150eb8..540c3343b2a1b 100644
--- a/pandas/tests/arrays/test_timedeltas.py
+++ b/pandas/tests/arrays/test_timedeltas.py
@@ -125,6 +125,22 @@ def test_setitem_clears_freq(self):
         a[0] = pd.Timedelta("1H")
         assert a.freq is None
 
+    @pytest.mark.parametrize(
+        "obj",
+        [
+            pd.Timedelta(seconds=1),
+            pd.Timedelta(seconds=1).to_timedelta64(),
+            pd.Timedelta(seconds=1).to_pytimedelta(),
+        ],
+    )
+    def test_setitem_objects(self, obj):
+        # make sure we accept timedelta64 and timedelta in addition to Timedelta
+        tdi = pd.timedelta_range("2 Days", periods=4, freq="H")
+        arr = TimedeltaArray(tdi, freq=tdi.freq)
+
+        arr[0] = obj
+        assert arr[0] == pd.Timedelta(seconds=1)
+
 
 class TestReductions:
     def test_min_max(self):
diff --git a/pandas/tests/test_base.py b/pandas/tests/test_base.py
index d75016824d6cf..c760c75e44f6b 100644
--- a/pandas/tests/test_base.py
+++ b/pandas/tests/test_base.py
@@ -418,7 +418,7 @@ def test_value_counts_unique_nunique_null(self, null_obj):
                     values = o._shallow_copy(v)
                 else:
                     o = o.copy()
-                    o[0:2] = iNaT
+                    o[0:2] = pd.NaT
                     values = o._values
 
             elif needs_i8_conversion(o):