diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index d8609737b8c7a..451cba732ff60 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -698,7 +698,7 @@ Strings
 
 Interval
 ^^^^^^^^
--
+- Bug in :meth:`IntervalIndex.is_overlapping` incorrect output if interval has duplicate left boundaries (:issue:`49581`)
 -
 
 Indexing
diff --git a/pandas/_libs/intervaltree.pxi.in b/pandas/_libs/intervaltree.pxi.in
index e7a310513d2fa..0d7c96a6f2f2b 100644
--- a/pandas/_libs/intervaltree.pxi.in
+++ b/pandas/_libs/intervaltree.pxi.in
@@ -81,7 +81,8 @@ cdef class IntervalTree(IntervalMixin):
         """How to sort the left labels; this is used for binary search
         """
         if self._left_sorter is None:
-            self._left_sorter = np.argsort(self.left)
+            values = [self.right, self.left]
+            self._left_sorter = np.lexsort(values)
         return self._left_sorter
 
     @property
diff --git a/pandas/tests/indexes/interval/test_interval.py b/pandas/tests/indexes/interval/test_interval.py
index c8d7470032e5f..98c21fad1f8c2 100644
--- a/pandas/tests/indexes/interval/test_interval.py
+++ b/pandas/tests/indexes/interval/test_interval.py
@@ -791,6 +791,13 @@ def test_is_overlapping(self, start, shift, na_value, closed):
         result = index.is_overlapping
         assert result is expected
 
+        # intervals with duplicate left values
+        a = [10, 15, 20, 25, 30, 35, 40, 45, 45, 50, 55, 60, 65, 70, 75, 80, 85]
+        b = [15, 20, 25, 30, 35, 40, 45, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90]
+        index = IntervalIndex.from_arrays(a, b, closed="right")
+        result = index.is_overlapping
+        assert result is False
+
     @pytest.mark.parametrize(
         "tuples",
         [