diff --git a/.github/workflows/test-install-kustomize.yml b/.github/workflows/test-install-kustomize.yml
index ecbee3bccd..934c77a2c6 100644
--- a/.github/workflows/test-install-kustomize.yml
+++ b/.github/workflows/test-install-kustomize.yml
@@ -15,9 +15,6 @@ on:
 permissions:
   contents: read
 
-env:
-  expected_kustomize_version: v5.8.1
-
 jobs:
   test-install-kustomize:
     name: Test install_kustomize.sh (${{ matrix.release-file }})
@@ -25,9 +22,14 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        release-file:
-          - hack/test-files/minimized-release.json
-          - hack/test-files/unminimized-release.json
+        include:
+          - release-file: hack/test-files/minimized-release.json
+            expected-version: v5.8.1
+          - release-file: hack/test-files/unminimized-release.json
+            expected-version: v5.8.1
+          - release-file: hack/test-files/legacy-release.json
+            requested-version: 2.0.3
+            expected-version: KustomizeVersion:2.0.3
 
     steps:
       - name: Check out code
@@ -39,12 +41,17 @@ jobs:
           set -euo pipefail
           tmp_dir="$(mktemp -d)"
 
-          ./hack/install_kustomize.sh "$tmp_dir"
+          if [ -n "${requested_kustomize_version}" ]; then
+            ./hack/install_kustomize.sh "${requested_kustomize_version}" "$tmp_dir"
+          else
+            ./hack/install_kustomize.sh "$tmp_dir"
+          fi
 
           actual_kustomize_version=$("$tmp_dir/kustomize" version)
 
           echo "Kustomize version: ${actual_kustomize_version}"
-          [ "${actual_kustomize_version}" = "${expected_kustomize_version}" ] || (echo "Unexpected Kustomize version: Expected ${expected_kustomize_version}, got ${actual_kustomize_version}" && exit 1)
+          [[ "${actual_kustomize_version}" == *"${expected_kustomize_version}"* ]] || (echo "Unexpected Kustomize version: Expected ${expected_kustomize_version}, got ${actual_kustomize_version}" && exit 1)
         env:
-          expected_kustomize_version: ${{ env.expected_kustomize_version }}
+          requested_kustomize_version: ${{ matrix.requested-version }}
+          expected_kustomize_version: ${{ matrix.expected-version }}
           releases_file: ${{ github.workspace }}/${{ matrix.release-file }}
diff --git a/hack/install_kustomize.sh b/hack/install_kustomize.sh
index b504df8321..5d464e9dda 100755
--- a/hack/install_kustomize.sh
+++ b/hack/install_kustomize.sh
@@ -28,11 +28,33 @@ unset CDPATH
 
 where=$PWD
 
+function is_legacy_release {
+  local requested=$1
+  # Kustomize releases published before the kustomize/ tag prefix was introduced.
+  local unprefixed_tags=(
+    v1.0.0 v1.0.1 v1.0.2 v1.0.3 v1.0.4 v1.0.5 v1.0.6 v1.0.7 v1.0.8 v1.0.9 v1.0.10 v1.0.11
+    v2.0.0 v2.0.1 v2.0.2 v2.0.3 v2.1.0
+    v3.0.0 v3.0.1 v3.0.2 v3.0.3 v3.1.0 v3.2.0
+  )
+
+  local tag
+  for tag in "${unprefixed_tags[@]}"; do
+    if [[ "$tag" == "$requested" ]]; then
+      return 0
+    fi
+  done
+  return 1
+}
+
 release_url=https://api.github.com/repos/kubernetes-sigs/kustomize/releases
 if [ -n "$1" ]; then
   if [[ "$1" =~ ^[0-9]+(\.[0-9]+){2}$ ]]; then
     version=v$1
-    release_url=${release_url}/tags/kustomize%2F$version
+    if is_legacy_release "$version"; then
+      release_url=${release_url}/tags/$version
+    else
+      release_url=${release_url}/tags/kustomize%2F$version
+    fi
   elif [ -n "$2" ]; then
     echo "The first argument should be the requested version."
     exit 1
@@ -171,9 +193,15 @@ if [[ -z "$RELEASE_URL" ]]; then
   exit 1
 fi
 
-curl -sLO "$RELEASE_URL"
+download_file="${RELEASE_URL##*/}"
+curl -sL "$RELEASE_URL" -o "$download_file"
 
-tar xzf ./kustomize_v*_${opsys}_${arch}.tar.gz
+if [[ "$download_file" == *.tar.gz ]]; then
+  tar xzf "$download_file"
+else
+  mv "$download_file" kustomize
+  chmod +x kustomize
+fi
 
 cp ./kustomize "$where"
 
diff --git a/hack/test-files/legacy-release.json b/hack/test-files/legacy-release.json
new file mode 100644
index 0000000000..b81b62a3ae
--- /dev/null
+++ b/hack/test-files/legacy-release.json
@@ -0,0 +1,7 @@
+{
+  "assets": [
+    {
+      "browser_download_url": "https://github.com/kubernetes-sigs/kustomize/releases/download/v2.0.3/kustomize_2.0.3_linux_amd64"
+    }
+  ]
+}