diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 7ba64f57be136..6987292eaf05c 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -271,6 +271,7 @@ Numeric
 - Bug in :func:`to_numeric` where float precision was incorrect (:issue:`31364`)
 - Bug in :meth:`DataFrame.any` with ``axis=1`` and ``bool_only=True`` ignoring the ``bool_only`` keyword (:issue:`32432`)
 - Bug in :meth:`Series.equals` where a ``ValueError`` was raised when numpy arrays were compared to scalars (:issue:`35267`)
+- Bug in :class:`Series` where two :class:`Series` each have a :class:`DatetimeIndex` with different timezones having those indexes incorrectly changed when performing arithmetic operations (:issue:`33671`)
 -
 
 Conversion
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 0b9021b094cd7..a8b48f875c825 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -8748,6 +8748,10 @@ def _align_frame(
         if is_datetime64tz_dtype(left.index.dtype):
             if left.index.tz != right.index.tz:
                 if join_index is not None:
+                    # GH#33671 ensure we don't change the index on
+                    #  our original Series (NB: by default deep=False)
+                    left = left.copy()
+                    right = right.copy()
                     left.index = join_index
                     right.index = join_index
 
@@ -8835,6 +8839,10 @@ def _align_series(
             if is_datetime64tz_dtype(left.index.dtype):
                 if left.index.tz != right.index.tz:
                     if join_index is not None:
+                        # GH#33671 ensure we don't change the index on
+                        #  our original Series (NB: by default deep=False)
+                        left = left.copy()
+                        right = right.copy()
                         left.index = join_index
                         right.index = join_index
 
diff --git a/pandas/tests/series/test_arithmetic.py b/pandas/tests/series/test_arithmetic.py
index 8fad6ee1cca8b..f30246ff12fac 100644
--- a/pandas/tests/series/test_arithmetic.py
+++ b/pandas/tests/series/test_arithmetic.py
@@ -254,6 +254,19 @@ def test_sub_datetimelike_align(self):
         result = (dt2.to_frame() - dt.to_frame())[0]
         tm.assert_series_equal(result, expected)
 
+    def test_alignment_doesnt_change_tz(self):
+        # GH#33671
+        dti = pd.date_range("2016-01-01", periods=10, tz="CET")
+        dti_utc = dti.tz_convert("UTC")
+        ser = pd.Series(10, index=dti)
+        ser_utc = pd.Series(10, index=dti_utc)
+
+        # we don't care about the result, just that original indexes are unchanged
+        ser * ser_utc
+
+        assert ser.index is dti
+        assert ser_utc.index is dti_utc
+
 
 # ------------------------------------------------------------------
 # Comparisons