diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 03ad8ed162c95..17d6226d2c60a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -210,6 +210,7 @@ Other enhancements
 - :meth:`Series.map` can now accept kwargs to pass on to func (:issue:`59814`)
 - :meth:`Series.map` now accepts an ``engine`` parameter to allow execution with a third-party execution engine (:issue:`61125`)
 - :meth:`Series.rank` and :meth:`DataFrame.rank` with numpy-nullable dtypes preserve ``NA`` values and return ``UInt64`` dtype where appropriate instead of casting ``NA`` to ``NaN`` with ``float64`` dtype (:issue:`62043`)
+- :meth:`Series.round` now operates pointwise on columns of object dtype (:issue:`62174`)
 - :meth:`Series.str.get_dummies` now accepts a  ``dtype`` parameter to specify the dtype of the resulting DataFrame (:issue:`47872`)
 - :meth:`pandas.concat` will raise a ``ValueError`` when ``ignore_index=True`` and ``keys`` is not ``None`` (:issue:`59274`)
 - :py:class:`frozenset` elements in pandas objects are now natively printed (:issue:`60690`)
diff --git a/pandas/core/series.py b/pandas/core/series.py
index b40e71f2b5b42..7548b29bb28ea 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -2514,7 +2514,14 @@ def round(self, decimals: int = 0, *args, **kwargs) -> Series:
         """
         nv.validate_round(args, kwargs)
         if self.dtype == "object":
-            raise TypeError("Expected numeric dtype, got object instead.")
+            try:
+                round_func = functools.partial(round, ndigits=decimals)
+                new_values = self._map_values(round_func)
+                return self._constructor(
+                    new_values, index=self.index, copy=False
+                ).__finalize__(self, method="map")
+            except TypeError as e:
+                raise TypeError("Expected numeric entries for dtype object.") from e
         new_mgr = self._mgr.round(decimals=decimals)
         return self._constructor_from_mgr(new_mgr, axes=new_mgr.axes).__finalize__(
             self, method="round"
diff --git a/pandas/tests/series/methods/test_round.py b/pandas/tests/series/methods/test_round.py
index a78f77e990ae1..9f13cc5efa0c1 100644
--- a/pandas/tests/series/methods/test_round.py
+++ b/pandas/tests/series/methods/test_round.py
@@ -74,8 +74,11 @@ def test_round_ea_boolean(self):
         tm.assert_series_equal(ser, expected)
 
     def test_round_dtype_object(self):
-        # GH#61206
-        ser = Series([0.2], dtype="object")
-        msg = "Expected numeric dtype, got object instead."
+        # GH#61206, GH#62174
+        ser = Series([0.232], dtype="object")
+        expected = Series([0.2])
+        tm.assert_series_equal(ser.round(1), expected)
+        ser2 = Series(["bar"], dtype="object")
+        msg = "Expected numeric entries for dtype object."
         with pytest.raises(TypeError, match=msg):
-            ser.round()
+            ser2.round()