diff --git a/src/net/http/export_test.go b/src/net/http/export_test.go
index f57e0c1585..1825acd9be 100644
--- a/src/net/http/export_test.go
+++ b/src/net/http/export_test.go
@@ -211,3 +211,9 @@ func (s *Server) ExportAllConnsIdle() bool {
 func (r *Request) WithT(t *testing.T) *Request {
 	return r.WithContext(context.WithValue(r.Context(), tLogKey{}, t.Logf))
 }
+
+func ExportSetH2GoawayTimeout(d time.Duration) (restore func()) {
+	old := http2goAwayTimeout
+	http2goAwayTimeout = d
+	return func() { http2goAwayTimeout = old }
+}
diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index 174f6845aa..1ffa411500 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -5447,7 +5447,11 @@ func TestServerCloseDeadlock(t *testing.T) {
 func TestServerKeepAlivesEnabled_h1(t *testing.T) { testServerKeepAlivesEnabled(t, h1Mode) }
 func TestServerKeepAlivesEnabled_h2(t *testing.T) { testServerKeepAlivesEnabled(t, h2Mode) }
 func testServerKeepAlivesEnabled(t *testing.T, h2 bool) {
-	setParallel(t)
+	if h2 {
+		restore := ExportSetH2GoawayTimeout(10 * time.Millisecond)
+		defer restore()
+	}
+	// Not parallel: messes with global variable. (http2goAwayTimeout)
 	defer afterTest(t)
 	cst := newClientServerTest(t, h2, HandlerFunc(func(w ResponseWriter, r *Request) {
 		fmt.Fprintf(w, "%v", r.RemoteAddr)