diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 087db014de5b3..0ede340720922 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2310,11 +2310,11 @@ def _union(self, other, sort):
             return other._get_reconciled_name_object(self)
 
         # TODO(EA): setops-refactor, clean all this up
-        if is_period_dtype(self) or is_datetime64tz_dtype(self):
+        if is_datetime64tz_dtype(self):
             lvals = self._ndarray_values
         else:
             lvals = self._values
-        if is_period_dtype(other) or is_datetime64tz_dtype(other):
+        if is_datetime64tz_dtype(other):
             rvals = other._ndarray_values
         else:
             rvals = other._values
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index f61721a0e51e6..0c709e562517b 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -388,6 +388,8 @@ def values(self):
 
     def _wrap_setop_result(self, other, result):
         name = get_op_result_name(self, other)
+        # We use _shallow_copy rather than the Index implementation
+        #  (which uses _constructor) in order to preserve dtype.
         return self._shallow_copy(result, name=name)
 
     @Appender(_index_shared_docs["contains"] % _index_doc_kwargs)
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 1fed0201f7b2b..89ae665c36376 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -768,12 +768,6 @@ def _assert_can_do_setop(self, other):
         if isinstance(other, PeriodIndex) and self.freq != other.freq:
             raise raise_on_incompatible(self, other)
 
-    def _wrap_setop_result(self, other, result):
-        name = get_op_result_name(self, other)
-        result = self._apply_meta(result)
-        result.name = name
-        return result
-
     def intersection(self, other, sort=False):
         self._validate_sort_keyword(sort)
         self._assert_can_do_setop(other)
@@ -819,6 +813,26 @@ def difference(self, other, sort=None):
         result = self._shallow_copy(np.asarray(i8result, dtype=np.int64), name=res_name)
         return result
 
+    def _union(self, other, sort):
+        if not len(other) or self.equals(other) or not len(self):
+            return super()._union(other, sort=sort)
+
+        # We are called by `union`, which is responsible for this validation
+        assert isinstance(other, type(self))
+
+        if not is_dtype_equal(self.dtype, other.dtype):
+            this = self.astype("O")
+            other = other.astype("O")
+            return this._union(other, sort=sort)
+
+        i8self = Int64Index._simple_new(self.asi8)
+        i8other = Int64Index._simple_new(other.asi8)
+        i8result = i8self._union(i8other, sort=sort)
+
+        res_name = get_op_result_name(self, other)
+        result = self._shallow_copy(np.asarray(i8result, dtype=np.int64), name=res_name)
+        return result
+
     # ------------------------------------------------------------------------
 
     def _apply_meta(self, rawarr):