diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 64ba18271100e..f23366193958f 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3410,7 +3410,7 @@ def get_indexer(
         if len(target) == 0:
             return np.array([], dtype=np.intp)
 
-        if not self._should_compare(target) and not is_interval_dtype(self.dtype):
+        if not self._should_compare(target) and not self._should_partial_index(target):
             # IntervalIndex get special treatment bc numeric scalars can be
             #  matched to Interval scalars
             return self._get_indexer_non_comparable(target, method=method, unique=True)
@@ -3478,6 +3478,16 @@ def _get_indexer(
 
         return ensure_platform_int(indexer)
 
+    @final
+    def _should_partial_index(self, target: Index) -> bool:
+        """
+        Should we attempt partial-matching indexing?
+        """
+        if is_interval_dtype(self.dtype):
+            # "Index" has no attribute "left"
+            return self.left._should_compare(target)  # type: ignore[attr-defined]
+        return False
+
     @final
     def _check_indexing_method(
         self,
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index e6764dd01e6d3..9225f128d1f26 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -646,9 +646,6 @@ def _get_indexer(
         # returned ndarray is np.intp
 
         if isinstance(target, IntervalIndex):
-            if not self._should_compare(target):
-                return self._get_indexer_non_comparable(target, method, unique=True)
-
             # non-overlapping -> at most one match per interval in target
             # want exact matches -> need both left/right to match, so defer to
             # left/right get_indexer, compare elementwise, equality -> match
@@ -656,12 +653,14 @@ def _get_indexer(
             right_indexer = self.right.get_indexer(target.right)
             indexer = np.where(left_indexer == right_indexer, left_indexer, -1)
 
-        elif not is_object_dtype(target):
+        elif not is_object_dtype(target.dtype):
             # homogeneous scalar index: use IntervalTree
+            # we should always have self._should_partial_index(target) here
             target = self._maybe_convert_i8(target)
             indexer = self._engine.get_indexer(target.values)
         else:
             # heterogeneous scalar index: defer elementwise to get_loc
+            # we should always have self._should_partial_index(target) here
             return self._get_indexer_pointwise(target)[0]
 
         return ensure_platform_int(indexer)
@@ -671,11 +670,12 @@ def get_indexer_non_unique(self, target: Index) -> tuple[np.ndarray, np.ndarray]
         # both returned ndarrays are np.intp
         target = ensure_index(target)
 
-        if isinstance(target, IntervalIndex) and not self._should_compare(target):
-            # different closed or incompatible subtype -> no matches
+        if not self._should_compare(target) and not self._should_partial_index(target):
+            # e.g. IntervalIndex with different closed or incompatible subtype
+            #  -> no matches
             return self._get_indexer_non_comparable(target, None, unique=False)
 
-        elif is_object_dtype(target.dtype) or isinstance(target, IntervalIndex):
+        elif is_object_dtype(target.dtype) or not self._should_partial_index(target):
             # target might contain intervals: defer elementwise to get_loc
             return self._get_indexer_pointwise(target)