diff --git a/Tests/test_imagepalette.py b/Tests/test_imagepalette.py
index 10b89a2c0c2..526beb656e8 100644
--- a/Tests/test_imagepalette.py
+++ b/Tests/test_imagepalette.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from io import BytesIO
+import io
 from pathlib import Path
 
 import pytest
@@ -23,6 +23,13 @@ def test_reload() -> None:
         assert_image_equal(im.convert("RGB"), original.convert("RGB"))
 
 
+def test_save_fp() -> None:
+    palette = ImagePalette.ImagePalette()
+    with io.StringIO() as fp:
+        palette.save(fp)
+        assert not fp.closed
+
+
 def test_getcolor() -> None:
     palette = ImagePalette.ImagePalette()
     assert len(palette.palette) == 0
@@ -204,7 +211,7 @@ def test_2bit_palette(tmp_path: Path) -> None:
 
 
 def test_getpalette() -> None:
-    b = BytesIO(b"0 1\n1 2 3 4")
+    b = io.BytesIO(b"0 1\n1 2 3 4")
     p = PaletteFile.PaletteFile(b)
 
     palette, rawmode = p.getpalette()
@@ -216,6 +223,6 @@ def test_invalid_palette() -> None:
     with pytest.raises(OSError):
         ImagePalette.load("Tests/images/hopper.jpg")
 
-    b = BytesIO(b"1" * 101)
+    b = io.BytesIO(b"1" * 101)
     with pytest.raises(SyntaxError, match="bad palette file"):
         PaletteFile.PaletteFile(b)
diff --git a/src/PIL/ImagePalette.py b/src/PIL/ImagePalette.py
index eae7aea8fc3..99ad2771b4b 100644
--- a/src/PIL/ImagePalette.py
+++ b/src/PIL/ImagePalette.py
@@ -191,19 +191,24 @@ def save(self, fp: str | IO[str]) -> None:
         if self.rawmode:
             msg = "palette contains raw palette data"
             raise ValueError(msg)
+        open_fp = False
         if isinstance(fp, str):
             fp = open(fp, "w")
-        fp.write("# Palette\n")
-        fp.write(f"# Mode: {self.mode}\n")
-        for i in range(256):
-            fp.write(f"{i}")
-            for j in range(i * len(self.mode), (i + 1) * len(self.mode)):
-                try:
-                    fp.write(f" {self.palette[j]}")
-                except IndexError:
-                    fp.write(" 0")
-            fp.write("\n")
-        fp.close()
+            open_fp = True
+        try:
+            fp.write("# Palette\n")
+            fp.write(f"# Mode: {self.mode}\n")
+            for i in range(256):
+                fp.write(f"{i}")
+                for j in range(i * len(self.mode), (i + 1) * len(self.mode)):
+                    try:
+                        fp.write(f" {self.palette[j]}")
+                    except IndexError:
+                        fp.write(" 0")
+                fp.write("\n")
+        finally:
+            if open_fp:
+                fp.close()
 
 
 # --------------------------------------------------------------------