diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 219398f4071f5..c9675e0e1961a 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -553,6 +553,7 @@ Datetimelike
 - Bug in addition with a :class:`Tick` object and a ``np.timedelta64`` object incorrectly raising instead of returning :class:`Timedelta` (:issue:`44474`)
 - Bug in adding a ``np.timedelta64`` object to a :class:`BusinessDay` or :class:`CustomBusinessDay` object incorrectly raising (:issue:`44532`)
 - Bug in :meth:`Index.insert` for inserting ``np.datetime64``, ``np.timedelta64`` or ``tuple`` into :class:`Index` with ``dtype='object'`` with negative loc adding ``None`` and replacing existing value (:issue:`44509`)
+- Bug in :meth:`Series.mode` with ``DatetimeTZDtype`` incorrectly returning timezone-naive and ``PeriodDtype`` incorrectly raising (:issue:`41927`)
 -
 
 Timedelta
diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 763e76f8497fa..538d9b0348d5f 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -215,7 +215,7 @@ def _reconstruct_data(
         if isinstance(values, cls) and values.dtype == dtype:
             return values
 
-        values = cls._from_sequence(values)
+        values = cls._from_sequence(values, dtype=dtype)
     elif is_bool_dtype(dtype):
         values = values.astype(dtype, copy=False)
 
@@ -960,15 +960,18 @@ def mode(values, dropna: bool = True) -> Series:
     original = values
 
     # categorical is a fast-path
-    if is_categorical_dtype(values):
+    if is_categorical_dtype(values.dtype):
         if isinstance(values, Series):
             # TODO: should we be passing `name` below?
             return Series(values._values.mode(dropna=dropna), name=values.name)
         return values.mode(dropna=dropna)
 
-    if dropna and needs_i8_conversion(values.dtype):
-        mask = values.isnull()
-        values = values[~mask]
+    if needs_i8_conversion(values.dtype):
+        if dropna:
+            mask = values.isna()
+            values = values[~mask]
+        modes = mode(values.view("i8"))
+        return modes.view(original.dtype)
 
     values = _ensure_data(values)
 
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 6c6caac955efc..ffa31b4f66211 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -1972,7 +1972,7 @@ def count(self, level=None):
             self, method="count"
         )
 
-    def mode(self, dropna=True) -> Series:
+    def mode(self, dropna: bool = True) -> Series:
         """
         Return the mode(s) of the Series.
 
diff --git a/pandas/tests/series/test_reductions.py b/pandas/tests/series/test_reductions.py
index ca30e8f1ee6fd..c5b0428131973 100644
--- a/pandas/tests/series/test_reductions.py
+++ b/pandas/tests/series/test_reductions.py
@@ -7,6 +7,28 @@
     Series,
 )
 import pandas._testing as tm
+from pandas.core.algorithms import mode
+
+
+@pytest.mark.parametrize("as_period", [True, False])
+def test_mode_extension_dtype(as_period):
+    # GH#41927 preserve dt64tz dtype
+    ser = Series([pd.Timestamp(1979, 4, n) for n in range(1, 5)])
+
+    if as_period:
+        ser = ser.dt.to_period("D")
+    else:
+        ser = ser.dt.tz_localize("US/Central")
+
+    res = ser.mode()
+    assert res.dtype == ser.dtype
+    tm.assert_series_equal(res, ser)
+
+    res = mode(ser._values)
+    tm.assert_series_equal(res, ser)
+
+    res = mode(pd.Index(ser))
+    tm.assert_series_equal(res, ser)
 
 
 def test_reductions_td64_with_nat():