diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 1286577748afa..907cc246163c8 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -339,6 +339,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupby.tshift` failing to raise ``ValueError`` when a frequency cannot be inferred for the index of a group (:issue:`35937`)
 - Bug in :meth:`DataFrame.groupby` does not always maintain column index name for ``any``, ``all``, ``bfill``, ``ffill``, ``shift`` (:issue:`29764`)
 - Bug in :meth:`DataFrameGroupBy.apply` raising error with ``np.nan`` group(s) when ``dropna=False`` (:issue:`35889`)
+- Bug where :meth:`DataFrame.replace` and :meth:`Series.replace` would fail when replacement value was of a different dtype but equal to values in the original object (:issue:`34871`).
 -
 
 Reshaping
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index eb5b887c8b0cb..abcdfcc4840a6 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -714,9 +714,13 @@ def replace(
         # retry
         if not self._can_hold_element(to_replace):
             if not isinstance(to_replace, list):
-                if inplace:
-                    return [self]
-                return [self.copy()]
+                return self.astype(object).replace(
+                    to_replace=to_replace,
+                    value=value,
+                    inplace=inplace,
+                    regex=regex,
+                    convert=convert,
+                )
 
             to_replace = [x for x in to_replace if self._can_hold_element(x)]
             if not len(to_replace):
diff --git a/pandas/tests/frame/methods/test_replace.py b/pandas/tests/frame/methods/test_replace.py
index a77753ed9f9d0..c028bbfe82894 100644
--- a/pandas/tests/frame/methods/test_replace.py
+++ b/pandas/tests/frame/methods/test_replace.py
@@ -1492,6 +1492,13 @@ def test_replace_with_duplicate_columns(self, replacement):
 
         tm.assert_frame_equal(result, expected)
 
+    def test_replace_equal_value_different_dtype(self):
+        # https://github.com/pandas-dev/pandas/issues/34871
+        df = pd.DataFrame([1, 2, 3])
+        result = df.replace(1.0, 0)
+        expected = pd.DataFrame([0, 2, 3])
+        tm.assert_frame_equal(result, expected)
+
     @pytest.mark.xfail(
         reason="replace() changes dtype from period to object, see GH34871", strict=True
     )
diff --git a/pandas/tests/series/methods/test_replace.py b/pandas/tests/series/methods/test_replace.py
index e255d46e81851..8a6b51ef61875 100644
--- a/pandas/tests/series/methods/test_replace.py
+++ b/pandas/tests/series/methods/test_replace.py
@@ -442,6 +442,13 @@ def test_replace_extension_other(self):
         ser = pd.Series(pd.array([1, 2, 3], dtype="Int64"))
         ser.replace("", "")  # no exception
 
+    def test_replace_equal_value_different_dtype(self):
+        # https://github.com/pandas-dev/pandas/issues/34871
+        ser = pd.Series([1, 2, 3])
+        result = ser.replace(1.0, 0)
+        expected = pd.Series([0, 2, 3])
+        tm.assert_series_equal(result, expected)
+
     def test_replace_with_compiled_regex(self):
         # https://github.com/pandas-dev/pandas/issues/35680
         s = pd.Series(["a", "b", "c"])