diff --git a/doc/source/whatsnew/v1.1.1.rst b/doc/source/whatsnew/v1.1.1.rst
index c028fe6bea719..ff5bbccf63ffe 100644
--- a/doc/source/whatsnew/v1.1.1.rst
+++ b/doc/source/whatsnew/v1.1.1.rst
@@ -38,6 +38,7 @@ Bug fixes
 ~~~~~~~~~
 
 - Bug in ``Styler`` whereby `cell_ids` argument had no effect due to other recent changes (:issue:`35588`) (:issue:`35663`).
+- Bug in :func:`pandas.testing.assert_series_equal` and :func:`pandas.testing.assert_frame_equal` where extension dtypes were not ignored when ``check_dtypes`` was set to ``False`` (:issue:`35715`).
 
 Categorical
 ^^^^^^^^^^^
diff --git a/pandas/_testing.py b/pandas/_testing.py
index 713f29466f097..ef6232fa6d575 100644
--- a/pandas/_testing.py
+++ b/pandas/_testing.py
@@ -1377,12 +1377,18 @@ def assert_series_equal(
         )
     elif is_extension_array_dtype(left.dtype) and is_extension_array_dtype(right.dtype):
         assert_extension_array_equal(
-            left._values, right._values, index_values=np.asarray(left.index)
+            left._values,
+            right._values,
+            check_dtype=check_dtype,
+            index_values=np.asarray(left.index),
         )
     elif needs_i8_conversion(left.dtype) or needs_i8_conversion(right.dtype):
         # DatetimeArray or TimedeltaArray
         assert_extension_array_equal(
-            left._values, right._values, index_values=np.asarray(left.index)
+            left._values,
+            right._values,
+            check_dtype=check_dtype,
+            index_values=np.asarray(left.index),
         )
     else:
         _testing.assert_almost_equal(
diff --git a/pandas/tests/util/test_assert_extension_array_equal.py b/pandas/tests/util/test_assert_extension_array_equal.py
index d9fdf1491c328..f9259beab5d13 100644
--- a/pandas/tests/util/test_assert_extension_array_equal.py
+++ b/pandas/tests/util/test_assert_extension_array_equal.py
@@ -1,6 +1,7 @@
 import numpy as np
 import pytest
 
+from pandas import array
 import pandas._testing as tm
 from pandas.core.arrays.sparse import SparseArray
 
@@ -102,3 +103,11 @@ def test_assert_extension_array_equal_non_extension_array(side):
 
     with pytest.raises(AssertionError, match=msg):
         tm.assert_extension_array_equal(*args)
+
+
+@pytest.mark.parametrize("right_dtype", ["Int32", "int64"])
+def test_assert_extension_array_equal_ignore_dtype_mismatch(right_dtype):
+    # https://github.com/pandas-dev/pandas/issues/35715
+    left = array([1, 2, 3], dtype="Int64")
+    right = array([1, 2, 3], dtype=right_dtype)
+    tm.assert_extension_array_equal(left, right, check_dtype=False)
diff --git a/pandas/tests/util/test_assert_frame_equal.py b/pandas/tests/util/test_assert_frame_equal.py
index fe3e1ff906919..3aa3c64923b14 100644
--- a/pandas/tests/util/test_assert_frame_equal.py
+++ b/pandas/tests/util/test_assert_frame_equal.py
@@ -260,3 +260,11 @@ def test_assert_frame_equal_interval_dtype_mismatch():
 
     with pytest.raises(AssertionError, match=msg):
         tm.assert_frame_equal(left, right, check_dtype=True)
+
+
+@pytest.mark.parametrize("right_dtype", ["Int32", "int64"])
+def test_assert_frame_equal_ignore_extension_dtype_mismatch(right_dtype):
+    # https://github.com/pandas-dev/pandas/issues/35715
+    left = pd.DataFrame({"a": [1, 2, 3]}, dtype="Int64")
+    right = pd.DataFrame({"a": [1, 2, 3]}, dtype=right_dtype)
+    tm.assert_frame_equal(left, right, check_dtype=False)
diff --git a/pandas/tests/util/test_assert_series_equal.py b/pandas/tests/util/test_assert_series_equal.py
index a7b5aeac560e4..f3c66052b1904 100644
--- a/pandas/tests/util/test_assert_series_equal.py
+++ b/pandas/tests/util/test_assert_series_equal.py
@@ -296,3 +296,11 @@ def test_series_equal_exact_for_nonnumeric():
         tm.assert_series_equal(s1, s3, check_exact=True)
     with pytest.raises(AssertionError):
         tm.assert_series_equal(s3, s1, check_exact=True)
+
+
+@pytest.mark.parametrize("right_dtype", ["Int32", "int64"])
+def test_assert_series_equal_ignore_extension_dtype_mismatch(right_dtype):
+    # https://github.com/pandas-dev/pandas/issues/35715
+    left = pd.Series([1, 2, 3], dtype="Int64")
+    right = pd.Series([1, 2, 3], dtype=right_dtype)
+    tm.assert_series_equal(left, right, check_dtype=False)