diff --git a/test/browser/webgl_offscreen_framebuffer_swap_with_bad_state.c b/test/browser/webgl_offscreen_framebuffer_swap_with_bad_state.c
index 562841f24f3e9..759fb353485e0 100644
--- a/test/browser/webgl_offscreen_framebuffer_swap_with_bad_state.c
+++ b/test/browser/webgl_offscreen_framebuffer_swap_with_bad_state.c
@@ -28,8 +28,14 @@ int main() {
   EMSCRIPTEN_WEBGL_CONTEXT_HANDLE ctx = emscripten_webgl_create_context("#canvas", &attr);
   emscripten_webgl_make_context_current(ctx);
 
-#if !TEST_WEBGL2 && TEST_VAO
+#if !TEST_WEBGL2 && TEST_VERIFY_WEBGL1_VAO_SUPPORT
   // This test cannot run without browser support for OES_vertex_array_object.
+  // This check is just to verify that the browser has support; otherwise, we
+  // will end up testing the non-VAO path. Enabling it here does not actually do
+  // anything, because offscreen framebuffer has already been initialized. Note
+  // that if GL_SUPPORT_AUTOMATIC_ENABLE_EXTENSIONS=0, then offscreen
+  // framebuffer will _never_ use VAOs on WebGL 1 (unless something enables
+  // OES_vertex_array_object before createOffscreenFramebuffer runs).
   if (!emscripten_webgl_enable_extension(ctx, "OES_vertex_array_object")) {
     return 1;
   }
diff --git a/test/test_browser.py b/test/test_browser.py
index 3d6f309d6a121..89b7edbaa6740 100644
--- a/test/test_browser.py
+++ b/test/test_browser.py
@@ -4322,22 +4322,22 @@ def test_webgl_vao_without_automatic_extensions(self):
 
   # Tests that offscreen framebuffer state restoration works
   @requires_graphics_hardware
-  def test_webgl_offscreen_framebuffer_state_restoration(self):
-    for args in [
-        # full state restoration path on WebGL 1.0
-        ['-sMAX_WEBGL_VERSION', '-sOFFSCREEN_FRAMEBUFFER_FORBID_VAO_PATH'],
-        # VAO path on WebGL 1.0
-        ['-sMAX_WEBGL_VERSION'],
-        ['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=0'],
-        # VAO path on WebGL 2.0
-        ['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=1', '-DTEST_REQUIRE_VAO=1'],
-        # full state restoration path on WebGL 2.0
-        ['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=1', '-sOFFSCREEN_FRAMEBUFFER_FORBID_VAO_PATH'],
-        # blitFramebuffer path on WebGL 2.0 (falls back to VAO on Firefox < 67)
-        ['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=0'],
-      ]:
-      cmd = args + ['-lGL', '-sOFFSCREEN_FRAMEBUFFER', '-DEXPLICIT_SWAP=1']
-      self.btest_exit('webgl_offscreen_framebuffer_swap_with_bad_state.c', args=cmd)
+  @parameterized({
+    # full state restoration path on WebGL 1.0
+    'gl1_no_vao': (['-sMAX_WEBGL_VERSION=1', '-sOFFSCREEN_FRAMEBUFFER_FORBID_VAO_PATH'],),
+    # VAO path on WebGL 1.0
+    'gl1': (['-sMAX_WEBGL_VERSION=1', '-DTEST_VERIFY_WEBGL1_VAO_SUPPORT=1'],),
+    'gl1_max_gl2': (['-sMAX_WEBGL_VERSION=2'],),
+    # VAO path on WebGL 2.0
+    'gl2': (['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=1'],),
+    # full state restoration path on WebGL 2.0
+    'gl2_no_vao': (['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=1', '-sOFFSCREEN_FRAMEBUFFER_FORBID_VAO_PATH'],),
+    # blitFramebuffer path on WebGL 2.0 (falls back to VAO on Firefox < 67)
+    'gl2_no_aa': (['-sMAX_WEBGL_VERSION=2', '-DTEST_WEBGL2=1', '-DTEST_ANTIALIAS=0'],),
+  })
+  def test_webgl_offscreen_framebuffer_state_restoration(self, args, skip_vao=False):
+    cmd = args + ['-lGL', '-sOFFSCREEN_FRAMEBUFFER', '-DEXPLICIT_SWAP=1']
+    self.btest_exit('webgl_offscreen_framebuffer_swap_with_bad_state.c', args=cmd)
 
   @parameterized({
     '': ([],),