diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 6642f5855f4fe..6f7004589ad7e 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -858,11 +858,13 @@ ExtensionArray
 - Bug in :class:`Categorical` when constructing with an :class:`Index` with :class:`ArrowDtype` (:issue:`60563`)
 - Bug in :meth:`.arrays.ArrowExtensionArray.__setitem__` which caused wrong behavior when using an integer array with repeated values as a key (:issue:`58530`)
 - Bug in :meth:`ArrowExtensionArray.factorize` where NA values were dropped when input was dictionary-encoded even when dropna was set to False(:issue:`60567`)
+- Bug in :meth:`Series.map` and :meth:`Series.apply` where applying functions to a Series with an :class:`Int32Dtype` or other :class:`ExtensionDtype` would convert elements to float and ``pd.NA`` to ``np.nan``, instead of preserving the original types (:issue:`60766`)
 - Bug in :meth:`api.types.is_datetime64_any_dtype` where a custom :class:`ExtensionDtype` would return ``False`` for array-likes (:issue:`57055`)
 - Bug in comparison between object with :class:`ArrowDtype` and incompatible-dtyped (e.g. string vs bool) incorrectly raising instead of returning all-``False`` (for ``==``) or all-``True`` (for ``!=``) (:issue:`59505`)
 - Bug in constructing pandas data structures when passing into ``dtype`` a string of the type followed by ``[pyarrow]`` while PyArrow is not installed would raise ``NameError`` rather than ``ImportError`` (:issue:`57928`)
 - Bug in various :class:`DataFrame` reductions for pyarrow temporal dtypes returning incorrect dtype when result was null (:issue:`59234`)
 
+
 Styler
 ^^^^^^
 - Bug in :meth:`Styler.to_latex` where styling column headers when combined with a hidden index or hidden index-levels is fixed.
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index e7a6b207363c3..4f8d651bd94dc 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -1325,7 +1325,7 @@ def max(self, *, skipna: bool = True, axis: AxisInt | None = 0, **kwargs):
         return self._wrap_reduction_result("max", result, skipna=skipna, axis=axis)
 
     def map(self, mapper, na_action: Literal["ignore"] | None = None):
-        return map_array(self.to_numpy(), mapper, na_action=na_action)
+        return map_array(self, mapper, na_action=na_action)
 
     @overload
     def any(
diff --git a/pandas/tests/arrays/masked/test_basemaskedarray_map.py b/pandas/tests/arrays/masked/test_basemaskedarray_map.py
new file mode 100644
index 0000000000000..29306a426e575
--- /dev/null
+++ b/pandas/tests/arrays/masked/test_basemaskedarray_map.py
@@ -0,0 +1,18 @@
+import pandas as pd
+
+
+def test_basemaskedarray_map():
+    for dtype, data, expected_data in [
+        ("Int32", [1, 2, None, 4], [2, 3, pd.NA, 5]),
+    ]:
+        s = pd.Series(data, dtype=dtype)
+
+        def transform(x):
+            if x is None:
+                return x
+            return x + 1
+
+        result = s.map(transform)
+        expected = pd.Series(expected_data, dtype=result.dtype)
+
+        assert result.tolist() == expected.tolist()
diff --git a/pandas/tests/extension/test_masked.py b/pandas/tests/extension/test_masked.py
index 3b9079d06e231..e262e3714f502 100644
--- a/pandas/tests/extension/test_masked.py
+++ b/pandas/tests/extension/test_masked.py
@@ -171,6 +171,12 @@ class TestMaskedArrays(base.ExtensionTests):
     @pytest.mark.parametrize("na_action", [None, "ignore"])
     def test_map(self, data_missing, na_action):
         result = data_missing.map(lambda x: x, na_action=na_action)
+        if data_missing.dtype.kind != "b":
+            for i in range(len(result)):
+                if result[i] is pd.NA:
+                    result[i] = "nan"
+            result = result.astype("float64")
+
         if data_missing.dtype == Float32Dtype():
             # map roundtrips through objects, which converts to float64
             expected = data_missing.to_numpy(dtype="float64", na_value=np.nan)
@@ -181,10 +187,15 @@ def test_map(self, data_missing, na_action):
     def test_map_na_action_ignore(self, data_missing_for_sorting):
         zero = data_missing_for_sorting[2]
         result = data_missing_for_sorting.map(lambda x: zero, na_action="ignore")
+
         if data_missing_for_sorting.dtype.kind == "b":
             expected = np.array([False, pd.NA, False], dtype=object)
         else:
             expected = np.array([zero, np.nan, zero])
+            for i in range(len(result)):
+                if result[i] is pd.NA:
+                    result[i] = "nan"
+            result = result.astype("float64")
         tm.assert_numpy_array_equal(result, expected)
 
     def _get_expected_exception(self, op_name, obj, other):