diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 4c80a47209e..d755f6067a7 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -4334,9 +4334,9 @@ def rename_dims(
                     f"cannot rename {k!r} because it is not found "
                     f"in the dimensions of this dataset {tuple(self.dims)}"
                 )
-            if v in self.dims or v in self:
+            if v in self.dims:
                 raise ValueError(
-                    f"Cannot rename {k} to {v} because {v} already exists. "
+                    f"Cannot rename dimension {k} to {v} because dimension {v} already exists. "
                     "Try using swap_dims instead."
                 )
 
@@ -4464,33 +4464,16 @@ def swap_dims(
                     f"variable along the old dimension {current_name!r}"
                 )
 
-        result_dims = {dims_dict.get(dim, dim) for dim in self.dims}
+        result = self.rename_dims(dims_dict)
+        result = result.drop_indexes(dims_dict.keys(), errors="ignore")
+        for dim in dims_dict.values():
+            if dim in result._variables:
+                if dim not in result._coord_names:
+                    result = result.set_coords(dim)
+                if dim not in result._indexes:
+                    result = result.set_xindex(dim)
 
-        coord_names = self._coord_names.copy()
-        coord_names.update({dim for dim in dims_dict.values() if dim in self.variables})
-
-        variables: dict[Hashable, Variable] = {}
-        indexes: dict[Hashable, Index] = {}
-        for current_name, current_variable in self.variables.items():
-            dims = tuple(dims_dict.get(dim, dim) for dim in current_variable.dims)
-            var: Variable
-            if current_name in result_dims:
-                var = current_variable.to_index_variable()
-                var.dims = dims
-                if current_name in self._indexes:
-                    indexes[current_name] = self._indexes[current_name]
-                    variables[current_name] = var
-                else:
-                    index, index_vars = create_default_index_implicit(var)
-                    indexes.update({name: index for name in index_vars})
-                    variables.update(index_vars)
-                    coord_names.update(index_vars)
-            else:
-                var = current_variable.to_base_variable()
-                var.dims = dims
-                variables[current_name] = var
-
-        return self._replace_with_new_dims(variables, coord_names, indexes=indexes)
+        return result
 
     def expand_dims(
         self,
diff --git a/xarray/testing/assertions.py b/xarray/testing/assertions.py
index 6418eb79b8b..bb5b3576a00 100644
--- a/xarray/testing/assertions.py
+++ b/xarray/testing/assertions.py
@@ -273,7 +273,7 @@ def _assert_indexes_invariants_checks(
         if isinstance(index, PandasIndex):
             pd_index = index.index
             var = possible_coord_variables[k]
-            assert (index.dim,) == var.dims, (pd_index, var)
+            assert (index.dim,) == var.dims, (index, index.dim, var)
             if k == index.dim:
                 # skip multi-index levels here (checked below)
                 assert index.coord_dtype == var.dtype, (index.coord_dtype, var.dtype)
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index e2a64964775..47fe6600064 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -3251,6 +3251,13 @@ def test_swap_dims(self) -> None:
         assert isinstance(actual.variables["x"], Variable)
         assert actual.xindexes["y"].equals(expected.xindexes["y"])
 
+    def test_swap_dims_after_rename_vars(self) -> None:
+        # https://github.com/pydata/xarray/issues/8646
+        ds = Dataset(coords={"y": [1, 2]})
+        actual = ds.rename_vars(y="z").swap_dims(y="z")
+        expected = Dataset(coords={"z": [1, 2]})
+        assert_identical(actual, expected)
+
     def test_expand_dims_error(self) -> None:
         original = Dataset(
             {