diff --git a/src/net/http/export_test.go b/src/net/http/export_test.go
index 52bccbd..7952e00 100644
--- a/src/net/http/export_test.go
+++ b/src/net/http/export_test.go
@@ -59,9 +59,9 @@
 
 func NewTestTimeoutHandler(handler Handler, ch <-chan time.Time) Handler {
 	return &timeoutHandler{
-		handler: handler,
-		timeout: func() <-chan time.Time { return ch },
-		// (no body and nil cancelTimer)
+		handler:     handler,
+		testTimeout: ch,
+		// (no body)
 	}
 }
 
diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index 384b453..f79c045 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -1888,6 +1888,32 @@
 	}
 }
 
+// Issue 14568.
+func TestTimeoutHandlerStartTimerWhenServing(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping sleeping test in -short mode")
+	}
+	defer afterTest(t)
+	var handler HandlerFunc = func(w ResponseWriter, _ *Request) {
+		w.WriteHeader(StatusNoContent)
+	}
+	timeout := 300 * time.Millisecond
+	ts := httptest.NewServer(TimeoutHandler(handler, timeout, ""))
+	defer ts.Close()
+	// Issue was caused by the timeout handler starting the timer when
+	// was created, not when the request. So wait for more than the timeout
+	// to ensure that's not the case.
+	time.Sleep(2 * timeout)
+	res, err := Get(ts.URL)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer res.Body.Close()
+	if res.StatusCode != StatusNoContent {
+		t.Errorf("got res.StatusCode %d, want %v", res.StatusCode, StatusNoContent)
+	}
+}
+
 // Verifies we don't path.Clean() on the wrong parts in redirects.
 func TestRedirectMunging(t *testing.T) {
 	req, _ := NewRequest("GET", "http://example.com/", nil)
diff --git a/src/net/http/server.go b/src/net/http/server.go
index 5e3b608..f23ef73 100644
--- a/src/net/http/server.go
+++ b/src/net/http/server.go
@@ -2309,15 +2309,10 @@
 // TimeoutHandler buffers all Handler writes to memory and does not
 // support the Hijacker or Flusher interfaces.
 func TimeoutHandler(h Handler, dt time.Duration, msg string) Handler {
-	t := time.NewTimer(dt)
 	return &timeoutHandler{
 		handler: h,
 		body:    msg,
-
-		// Effectively storing a *time.Timer, but decomposed
-		// for testing:
-		timeout:     func() <-chan time.Time { return t.C },
-		cancelTimer: t.Stop,
+		dt:      dt,
 	}
 }
 
@@ -2328,12 +2323,11 @@
 type timeoutHandler struct {
 	handler Handler
 	body    string
+	dt      time.Duration
 
-	// timeout returns the channel of a *time.Timer and
-	// cancelTimer cancels it.  They're stored separately for
-	// testing purposes.
-	timeout     func() <-chan time.Time // returns channel producing a timeout
-	cancelTimer func() bool             // optional
+	// When set, no timer will be created and this channel will
+	// be used instead.
+	testTimeout <-chan time.Time
 }
 
 func (h *timeoutHandler) errorBody() string {
@@ -2344,6 +2338,12 @@
 }
 
 func (h *timeoutHandler) ServeHTTP(w ResponseWriter, r *Request) {
+	var t *time.Timer
+	timeout := h.testTimeout
+	if timeout == nil {
+		t = time.NewTimer(h.dt)
+		timeout = t.C
+	}
 	done := make(chan struct{})
 	tw := &timeoutWriter{
 		w: w,
@@ -2363,10 +2363,10 @@
 		}
 		w.WriteHeader(tw.code)
 		w.Write(tw.wbuf.Bytes())
-		if h.cancelTimer != nil {
-			h.cancelTimer()
+		if t != nil {
+			t.Stop()
 		}
-	case <-h.timeout():
+	case <-timeout:
 		tw.mu.Lock()
 		defer tw.mu.Unlock()
 		w.WriteHeader(StatusServiceUnavailable)