diff --git a/build/rust/download_rust_toolchain_aux.py b/build/rust/download_rust_toolchain_aux.py
index a5d87842428b..69ee7770b3dc 100755
--- a/build/rust/download_rust_toolchain_aux.py
+++ b/build/rust/download_rust_toolchain_aux.py
@@ -4,7 +4,6 @@
 # License, v. 2.0. If a copy of the MPL was not distributed with this file,
 # You can obtain one at https://mozilla.org/MPL/2.0/.
 
-import glob
 from urllib.error import HTTPError
 import os
 from pathlib import Path
@@ -20,27 +19,24 @@
     import build_rust
     RUST_TOOLCHAIN = build_rust.RUST_TOOLCHAIN_OUT_DIR
 
-BRAVE_PREFIX = '.brave-'
-PACKAGE = os.path.join(
-    RUST_TOOLCHAIN, f'{BRAVE_PREFIX}{build_rust_toolchain_aux.package_name()}')
-PATTERN = os.path.join(RUST_TOOLCHAIN, f'{BRAVE_PREFIX}*')
+BRAVE_RUST_TOOLCHAIN_AUX = os.path.join(RUST_TOOLCHAIN,
+                                        '.brave_rust_toolchain_aux')
 
 
 def is_download_needed():
-    return os.getenv('SKIP_DOWNLOAD_RUST_TOOLCHAIN_AUX',
-                     '0') != '1' and not Path(PACKAGE).exists()
+    if os.getenv('SKIP_DOWNLOAD_RUST_TOOLCHAIN_AUX', '0') == '1':
+        return False
 
+    package_name = ''
+    try:
+        with open(BRAVE_RUST_TOOLCHAIN_AUX) as file:
+            package_name = file.readline().rstrip()
+    except Exception:
+        pass
+    return package_name != build_rust_toolchain_aux.package_name()
 
-def maybe_remove_old_package():
-    if entries := glob.glob(PATTERN):
-        [entry] = entries
-        print(f'Removing {entry}')
-        os.unlink(entry)
-
-
-def install_new_package(src_dir):
-    print(f'Installing {PACKAGE}')
 
+def install_package(src_dir):
     rust_lld_path = os.path.join(RUST_TOOLCHAIN, 'bin',
                                  build_rust_toolchain_aux.RUST_LLD)
     wasm32_unknown_unknown_path = os.path.join(
@@ -51,7 +47,7 @@ def install_new_package(src_dir):
     Path(rust_lld_path).unlink(missing_ok=True)
     shutil.rmtree(wasm32_unknown_unknown_path, ignore_errors=True)
 
-    # move new artifacts to their final places
+    # move new artifacts into their final places
     shutil.move(os.path.join(src_dir, build_rust_toolchain_aux.RUST_LLD),
                 rust_lld_path)
     shutil.move(
@@ -59,20 +55,23 @@ def install_new_package(src_dir):
         wasm32_unknown_unknown_path)
 
 
+def save_package_name():
+    with open(BRAVE_RUST_TOOLCHAIN_AUX, 'w+') as file:
+        file.write(f'{build_rust_toolchain_aux.package_name()}\n')
+
+
 def main():
     if not is_download_needed():
         print(f'Skipping {Path(__file__).stem}')
         return
 
-    maybe_remove_old_package()
-
     with tempfile.TemporaryDirectory(dir=RUST_TOOLCHAIN) as temp_dir:
         try:
             deps.DownloadAndUnpack(
                 f'{deps_config.DEPS_PACKAGES_URL}/rust-toolchain-aux/{build_rust_toolchain_aux.package_name()}',
-                temp_dir,
-                output_file=PACKAGE)
-            install_new_package(temp_dir)
+                temp_dir)
+            install_package(temp_dir)
+            save_package_name()
         except HTTPError as error:
             if error.code == 403:
                 print("If you see this error message, "
@@ -80,7 +79,6 @@ def main():
                       "and doing a Chromium bump - please visit "
                       "https://ci.brave.com/view/rust and use your branch "
                       "to build the required Rust auxiliary package.")
-            os.unlink(PACKAGE)
             raise
 
 
diff --git a/script/deps.py b/script/deps.py
index 889f8000b817..5b644aecb9b1 100755
--- a/script/deps.py
+++ b/script/deps.py
@@ -70,15 +70,14 @@ def EnsureDirExists(path):
         os.makedirs(path)
 
 
-def DownloadAndUnpack(url, output_dir, output_file=None, path_prefix=None):
+def DownloadAndUnpack(url, output_dir, path_prefix=None):
     """Download an archive from url and extract into output_dir. If path_prefix
        is not None, only extract files whose paths within the archive start
        with path_prefix."""
-    with (open(output_file, 'w+b') if output_file else
-          tempfile.NamedTemporaryFile(delete=False)) as file:
+    with tempfile.NamedTemporaryFile(delete=False) as tmp_file:
         try:
-            DownloadUrl(url, file)
-            file.close()
+            DownloadUrl(url, tmp_file)
+            tmp_file.close()
             try:
                 os.unlink(output_dir)
             except OSError:
@@ -87,9 +86,9 @@ def DownloadAndUnpack(url, output_dir, output_file=None, path_prefix=None):
             EnsureDirExists(output_dir)
             if url.endswith('.zip'):
                 assert path_prefix is None
-                extract_zip(file.name, output_dir)
+                extract_zip(tmp_file.name, output_dir)
             else:
-                t = tarfile.open(file.name, mode='r:*')
+                t = tarfile.open(tmp_file.name, mode='r:*')
                 members = None
                 if path_prefix is not None:
                     members = [
@@ -98,5 +97,4 @@ def DownloadAndUnpack(url, output_dir, output_file=None, path_prefix=None):
                     ]
                 t.extractall(path=output_dir, members=members)
         finally:
-            if not output_file:
-                os.unlink(file.name)
+            os.unlink(tmp_file.name)