diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 4debd41de213f..78ee359397df5 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -297,6 +297,7 @@ Performance improvements
 ~~~~~~~~~~~~~~~~~~~~~~~~
 - :attr:`Categorical.categories` returns a :class:`RangeIndex` columns instead of an :class:`Index` if the constructed ``values`` was a ``range``. (:issue:`57787`)
 - :class:`DataFrame` returns a :class:`RangeIndex` columns when possible when ``data`` is a ``dict`` (:issue:`57943`)
+- :class:`Series` returns a :class:`RangeIndex` index when possible when ``data`` is a ``dict`` (:issue:`58118`)
 - :func:`concat` returns a :class:`RangeIndex` level in the :class:`MultiIndex` result when ``keys`` is a ``range`` or :class:`RangeIndex` (:issue:`57542`)
 - :meth:`RangeIndex.append` returns a :class:`RangeIndex` instead of a :class:`Index` when appending values that could continue the :class:`RangeIndex` (:issue:`57467`)
 - :meth:`Series.str.extract` returns a :class:`RangeIndex` columns instead of an :class:`Index` column when possible (:issue:`57542`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index a4b58445289ad..73e564f95cf65 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -7144,7 +7144,10 @@ def maybe_sequence_to_range(sequence) -> Any | range:
         return sequence
     if len(sequence) == 0:
         return range(0)
-    np_sequence = np.asarray(sequence, dtype=np.int64)
+    try:
+        np_sequence = np.asarray(sequence, dtype=np.int64)
+    except OverflowError:
+        return sequence
     diff = np_sequence[1] - np_sequence[0]
     if diff == 0:
         return sequence
diff --git a/pandas/core/series.py b/pandas/core/series.py
index ee496a355f6ca..967aea15fff60 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -132,6 +132,7 @@
     PeriodIndex,
     default_index,
     ensure_index,
+    maybe_sequence_to_range,
 )
 import pandas.core.indexes.base as ibase
 from pandas.core.indexes.multi import maybe_droplevels
@@ -538,8 +539,6 @@ def _init_dict(
         _data : BlockManager for the new Series
         index : index for the new Series
         """
-        keys: Index | tuple
-
         # Looking for NaN in dict doesn't work ({np.nan : 1}[float('nan')]
         # raises KeyError), so we iterate the entire dict, and align
         if data:
@@ -547,7 +546,7 @@ def _init_dict(
             # using generators in effects the performance.
             # Below is the new way of extracting the keys and values
 
-            keys = tuple(data.keys())
+            keys = maybe_sequence_to_range(tuple(data.keys()))
             values = list(data.values())  # Generating list of values- faster way
         elif index is not None:
             # fastpath for Series(data=None). Just use broadcasting a scalar
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 68737e86f0c6a..97faba532e94a 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -2251,3 +2251,9 @@ def test_series_with_complex_nan(input_list):
     result = Series(ser.array)
     assert ser.dtype == "complex128"
     tm.assert_series_equal(ser, result)
+
+
+def test_dict_keys_rangeindex():
+    result = Series({0: 1, 1: 2})
+    expected = Series([1, 2], index=RangeIndex(2))
+    tm.assert_series_equal(result, expected, check_index_type=True)