diff --git a/pkg/dart2wasm/docs/flutter_hhh_builds.md b/pkg/dart2wasm/docs/flutter_hhh_builds.md
index 8722b684583..5ffd0b265e4 100644
--- a/pkg/dart2wasm/docs/flutter_hhh_builds.md
+++ b/pkg/dart2wasm/docs/flutter_hhh_builds.md
@@ -67,7 +67,7 @@ their correct version using
 ```
 
 Then checkout the Dart version we want. If the commit is available in the Dart
-checkout from `<src>/third_party/dart` then one may
+checkout from `<src>/flutter/third_party/dart` then one may
 
 ```
 <src> % vim flutter/DEPS
@@ -80,13 +80,13 @@ checkout from `<src>/third_party/dart` then one may
 but for local development one may just
 
 ```
-<src> % cd third_party/dart
-<src>/third_party/dart % git checkout ...
+<src> % cd flutter/third_party/dart
+<src>/flutter/third_party/dart % git checkout ...
 ```
 
 Now we have to make some modification to ensure that the build of the platform
 file doesn't use the downloaded prebuilt SDK but the one in
-`<src>/third_party/dart`, we do that by applying the following patch:
+`<src>/flutter/third_party/dart`, we do that by applying the following patch:
 
 ```
 <src>/flutter % git diff
@@ -133,7 +133,7 @@ Build the normal Dart SDK in the same version as used in Flutter engine via
 `tools/build.py -mrelease create_sdk`
 
 NOTE: You can (after syncing dependencies with `gclient sync -D`) make
-`<src>/third_party/dart` a symlink to the normal Dart SDK you work on. That
+`<src>/flutter/third_party/dart` a symlink to the normal Dart SDK you work on. That
 avoids the need to keep the two in sync.
 
 ## Building a Flutter app (e.g. Wonderous)
diff --git a/tools/3xhead_flutter_hooks.sh b/tools/3xhead_flutter_hooks.sh
index 984a2dec41b..d7a86a75133 100755
--- a/tools/3xhead_flutter_hooks.sh
+++ b/tools/3xhead_flutter_hooks.sh
@@ -8,7 +8,7 @@
 # latest dart sdk, run this script to apply workarounds to the source code. It
 # may patch up the source code so the three HEADs work together correctly.
 #
-# Usage: src/third_party/dart/tools/3xhead_flutter_hooks.sh
+# Usage: src/flutter/third_party/dart/tools/3xhead_flutter_hooks.sh
 # (run inside the root of a flutter engine checkout)
 
 set -e
@@ -20,4 +20,4 @@ ensure_in_checkout_root
 
 # Copy changed dependencies from Dart DEPS to engine DEPS and update them in
 # checkout.
-src/third_party/dart/tools/patches/flutter-engine/apply.sh
+src/flutter/third_party/dart/tools/patches/flutter-engine/apply.sh
diff --git a/tools/bots/flutter/compile_flutter.sh b/tools/bots/flutter/compile_flutter.sh
index 4aaeb50891d..0ee171b1b89 100755
--- a/tools/bots/flutter/compile_flutter.sh
+++ b/tools/bots/flutter/compile_flutter.sh
@@ -58,12 +58,6 @@ git clone --single-branch -vv \
 
 pushd flutter
 bin/flutter config --no-analytics
-pinned_dart_sdk=$(cat bin/cache/dart-sdk/revision)
-patch=$checkout/tools/patches/flutter-engine/${pinned_dart_sdk}.flutter.patch
-if [ -e "$patch" ]; then
-  git apply $patch
-fi
-
 bin/flutter update-packages
 popd  # flutter
 
@@ -73,13 +67,15 @@ git clone --single-branch --depth=1 -vv \
 pushd src
 git clone --single-branch --branch main --depth=1 -vv \
     https://dart.googlesource.com/external/github.com/flutter/engine flutter
+pushd flutter
 mkdir -p third_party
 pushd third_party
 ln -s $checkout dart
 popd  # third_party
+popd  # flutter
 popd  # src
 
-./src/third_party/dart/tools/patches/flutter-engine/apply.sh || true
+./src/flutter/third_party/dart/tools/patches/flutter-engine/apply.sh || true
 
 mkdir flutter_patched_sdk
 
diff --git a/tools/patches/flutter-engine/apply.sh b/tools/patches/flutter-engine/apply.sh
index 2964ad86757..9705dfd1678 100755
--- a/tools/patches/flutter-engine/apply.sh
+++ b/tools/patches/flutter-engine/apply.sh
@@ -7,7 +7,7 @@
 # This script updates the flutter engine DEPS file with the
 # Dart SDK dependencies.
 #
-# Usage: src/third_party/dart/tools/patches/flutter-engine/apply.sh
+# Usage: src/flutter/third_party/dart/tools/patches/flutter-engine/apply.sh
 # (run inside the root of a flutter engine checkout)
 
 set -e
@@ -40,7 +40,7 @@ if [ $need_runhooks = true ]; then
   # DEPS file might have been patched with new version of packages that
   # Dart SDK depends on. Get information about dependencies from the
   # DEPS file and forcefully update checkouts of those dependencies.
-  gclient revinfo --ignore-dep-type=cipd | grep 'src/third_party/dart/third_party' | while read -r line; do
+  gclient revinfo --ignore-dep-type=cipd | grep 'src/flutter/third_party/dart/third_party' | while read -r line; do
     # revinfo would produce lines in the following format:
     #     path: git-url@tag-or-hash
     # Where no spaces occur inside path, git-url or tag-or-hash.
diff --git a/tools/patches/utils.sh b/tools/patches/utils.sh
index 681c707ed97..88da6c001fa 100644
--- a/tools/patches/utils.sh
+++ b/tools/patches/utils.sh
@@ -13,7 +13,7 @@ die() {
 
 ensure_in_checkout_root() {
   set -e
-  if [ ! -e src/third_party/dart ]; then
+  if [ ! -e src/flutter/third_party/dart ]; then
     die
   fi