diff --git a/.ci.yaml b/.ci.yaml
index 391da69293..3d39c8df70 100644
--- a/.ci.yaml
+++ b/.ci.yaml
@@ -238,9 +238,11 @@ targets:
       cores: "32"
       # Pigeon tests need Andoid deps (thus the Linux_android base) and
       # clang-format.
+      # web_benchmarks needs Chrome.
       dependencies: >-
         [
-          {"dependency": "clang", "version": "git_revision:5d5aba78dbbee75508f01bcaa69aedb2ab79065a"}
+          {"dependency": "clang", "version": "git_revision:5d5aba78dbbee75508f01bcaa69aedb2ab79065a"},
+          {"dependency": "chrome_and_driver", "version": "version:114.0"}
         ]
       channel: master
 
@@ -251,11 +253,11 @@ targets:
       version_file: flutter_stable.version
       target_file: linux_custom_package_tests.yaml
       cores: "32"
-      # Pigeon tests need Android deps (thus the Linux_android base) and
-      # clang-format.
+      # See comments on 'master' version above.
       dependencies: >-
         [
-          {"dependency": "clang", "version": "git_revision:5d5aba78dbbee75508f01bcaa69aedb2ab79065a"}
+          {"dependency": "clang", "version": "git_revision:5d5aba78dbbee75508f01bcaa69aedb2ab79065a"},
+          {"dependency": "chrome_and_driver", "version": "version:114.0"}
         ]
       channel: stable
 
diff --git a/.cirrus.yml b/.cirrus.yml
index 7a5bae288d..be85fc9c01 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -170,16 +170,3 @@ task:
         - else
         -   echo "This user does not have permission to run Firebase Test Lab tests."
         - fi
-    ### Web tasks ###
-    - name: web_benchmarks_test
-      env:
-        matrix:
-          CHROMIUM_BUILD: "950363" # Chromium 98.0.4758.0
-          CHROMIUM_BUILD: "1097615" # Chromium 111
-      << : *INSTALL_CHROME_LINUX
-      script:
-        - cd packages/web_benchmarks/testing/test_app
-        - flutter packages get
-        - cd ../..
-        - flutter packages get
-        - dart testing/web_benchmarks_test.dart
diff --git a/packages/web_benchmarks/tool/run_tests.dart b/packages/web_benchmarks/tool/run_tests.dart
new file mode 100644
index 0000000000..3e0fb09344
--- /dev/null
+++ b/packages/web_benchmarks/tool/run_tests.dart
@@ -0,0 +1,76 @@
+// Copyright 2013 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// ignore_for_file: avoid_print
+
+// Runs `dart test -p chrome` in the root of the cross_file package.
+//
+// Called from the custom-tests CI action.
+//
+// usage: dart run tool/run_tests.dart
+// (needs a `chrome` executable in $PATH, or a tweak to dart_test.yaml)
+import 'dart:async';
+import 'dart:io';
+import 'package:path/path.dart' as p;
+
+Future<void> main(List<String> args) async {
+  if (!Platform.isLinux) {
+    // The test was migrated from a Linux-only task, so this preserves behavior.
+    // If desired, it can be enabled for other platforms in the future.
+    print('Skipping for non-Linux host');
+    exit(0);
+  }
+
+  final Directory packageDir =
+      Directory(p.dirname(Platform.script.path)).parent;
+  final String testingAppDirPath =
+      p.join(packageDir.path, 'testing', 'test_app');
+
+  // Fetch the test app's dependencies.
+  int status = await _runProcess(
+    'flutter',
+    <String>[
+      'pub',
+      'get',
+    ],
+    workingDirectory: testingAppDirPath,
+  );
+  if (status != 0) {
+    exit(status);
+  }
+
+  // Run the tests.
+  status = await _runProcess(
+    'flutter',
+    <String>[
+      'test',
+      'testing',
+    ],
+    workingDirectory: packageDir.path,
+  );
+
+  exit(status);
+}
+
+Future<Process> _streamOutput(Future<Process> processFuture) async {
+  final Process process = await processFuture;
+  await Future.wait(<Future<void>>[
+    stdout.addStream(process.stdout),
+    stderr.addStream(process.stderr),
+  ]);
+  return process;
+}
+
+Future<int> _runProcess(
+  String command,
+  List<String> arguments, {
+  String? workingDirectory,
+}) async {
+  final Process process = await _streamOutput(Process.start(
+    command,
+    arguments,
+    workingDirectory: workingDirectory,
+  ));
+  return process.exitCode;
+}