diff --git a/scripts/integration-tests/e2e-create-react-app.sh b/scripts/integration-tests/e2e-create-react-app.sh
index 7922ac920b0d..02fb7f92b755 100755
--- a/scripts/integration-tests/e2e-create-react-app.sh
+++ b/scripts/integration-tests/e2e-create-react-app.sh
@@ -28,6 +28,13 @@ cd tmp/create-react-app || exit
 # This change replaces useBuiltIns: true with runtime: "classic"
 sed -i 's/useBuiltIns: true/runtime: "classic"/' packages/babel-preset-react-app/create.js
 
+# create-react-app throws if `@babel/eslint-parser` is not pinned, but we
+# must upgrade it for test purposes
+sed -i "s#'@babel/eslint-parser',##" packages/react-scripts/scripts/utils/verifyPackageTree.js
+
+# remove this line when https://github.com/facebook/create-react-app/pull/11216 gets merged
+sed -i "s#isESLintPluginEnabled && 'babel-eslint',##" packages/react-scripts/scripts/utils/verifyPackageTree.js
+
 bump_deps="$PWD/../../utils/bump-babel-dependencies.js"
 node "$bump_deps"
 for d in ./packages/*/