diff --git a/src/net/http/export_test.go b/src/net/http/export_test.go
index 657ff9d..67a74ae 100644
--- a/src/net/http/export_test.go
+++ b/src/net/http/export_test.go
@@ -274,6 +274,17 @@ func (s *Server) ExportAllConnsIdle() bool {
 	return true
 }
 
+func (s *Server) ExportAllConnsByState() map[ConnState]int {
+	states := map[ConnState]int{}
+	s.mu.Lock()
+	defer s.mu.Unlock()
+	for c := range s.activeConn {
+		st, _ := c.getState()
+		states[st] += 1
+	}
+	return states
+}
+
 func (r *Request) WithT(t *testing.T) *Request {
 	return r.WithContext(context.WithValue(r.Context(), tLogKey{}, t.Logf))
 }
diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index 5f56932..806272b 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -5519,16 +5519,23 @@ func TestServerSetKeepAlivesEnabledClosesConns(t *testing.T) {
 	}
 }
 
-func TestServerShutdown_h1(t *testing.T) { testServerShutdown(t, h1Mode) }
-func TestServerShutdown_h2(t *testing.T) { testServerShutdown(t, h2Mode) }
+func TestServerShutdown_h1(t *testing.T) {
+	testServerShutdown(t, h1Mode)
+}
+func TestServerShutdown_h2(t *testing.T) {
+	testServerShutdown(t, h2Mode)
+}
 
 func testServerShutdown(t *testing.T, h2 bool) {
 	setParallel(t)
 	defer afterTest(t)
 	var doShutdown func() // set later
+	var doStateCount func()
 	var shutdownRes = make(chan error, 1)
+	var statesRes = make(chan map[ConnState]int, 1)
 	var gotOnShutdown = make(chan struct{}, 1)
 	handler := HandlerFunc(func(w ResponseWriter, r *Request) {
+		doStateCount()
 		go doShutdown()
 		// Shutdown is graceful, so it should not interrupt
 		// this in-flight response. Add a tiny sleep here to
@@ -5545,6 +5552,9 @@ func testServerShutdown(t *testing.T, h2 bool) {
 	doShutdown = func() {
 		shutdownRes <- cst.ts.Config.Shutdown(context.Background())
 	}
+	doStateCount = func() {
+		statesRes <- cst.ts.Config.ExportAllConnsByState()
+	}
 	get(t, cst.c, cst.ts.URL) // calls t.Fail on failure
 
 	if err := <-shutdownRes; err != nil {
@@ -5556,6 +5566,10 @@ func testServerShutdown(t *testing.T, h2 bool) {
 		t.Errorf("onShutdown callback not called, RegisterOnShutdown broken?")
 	}
 
+	if states := <-statesRes; states[StateActive] != 1 {
+		t.Errorf("connection in wrong state, %v", states)
+	}
+
 	res, err := cst.c.Get(cst.ts.URL)
 	if err == nil {
 		res.Body.Close()
diff --git a/src/net/http/server.go b/src/net/http/server.go
index d41b5f6..14a6336 100644
--- a/src/net/http/server.go
+++ b/src/net/http/server.go
@@ -324,7 +324,7 @@ func (c *conn) hijackLocked() (rwc net.Conn, buf *bufio.ReadWriter, err error) {
 			return nil, nil, fmt.Errorf("unexpected Peek failure reading buffered byte: %v", err)
 		}
 	}
-	c.setState(rwc, StateHijacked)
+	c.setState(rwc, StateHijacked, runHooks)
 	return
 }
 
@@ -1737,7 +1737,12 @@ func validNextProto(proto string) bool {
 	return true
 }
 
-func (c *conn) setState(nc net.Conn, state ConnState) {
+const (
+	runHooks  = true
+	skipHooks = false
+)
+
+func (c *conn) setState(nc net.Conn, state ConnState, runHook bool) {
 	srv := c.server
 	switch state {
 	case StateNew:
@@ -1750,6 +1755,9 @@ func (c *conn) setState(nc net.Conn, state ConnState) {
 	}
 	packedState := uint64(time.Now().Unix()<<8) | uint64(state)
 	atomic.StoreUint64(&c.curState.atomic, packedState)
+	if !runHook {
+		return
+	}
 	if hook := srv.ConnState; hook != nil {
 		hook(nc, state)
 	}
@@ -1803,7 +1811,7 @@ func (c *conn) serve(ctx context.Context) {
 		}
 		if !c.hijacked() {
 			c.close()
-			c.setState(c.rwc, StateClosed)
+			c.setState(c.rwc, StateClosed, runHooks)
 		}
 	}()
 
@@ -1831,6 +1839,10 @@ func (c *conn) serve(ctx context.Context) {
 		if proto := c.tlsState.NegotiatedProtocol; validNextProto(proto) {
 			if fn := c.server.TLSNextProto[proto]; fn != nil {
 				h := initALPNRequest{ctx, tlsConn, serverHandler{c.server}}
+				// Mark freshly created HTTP/2 as active and prevent any server state hooks
+				// from being run on these connections. This prevents closeIdleConns from
+				// closing such connections. See issue https://golang.org/issue/39776.
+				c.setState(c.rwc, StateActive, skipHooks)
 				fn(c.server, tlsConn, h)
 			}
 			return
@@ -1851,7 +1863,7 @@ func (c *conn) serve(ctx context.Context) {
 		w, err := c.readRequest(ctx)
 		if c.r.remain != c.server.initialReadLimitSize() {
 			// If we read any bytes off the wire, we're active.
-			c.setState(c.rwc, StateActive)
+			c.setState(c.rwc, StateActive, runHooks)
 		}
 		if err != nil {
 			const errorHeaders = "\r\nContent-Type: text/plain; charset=utf-8\r\nConnection: close\r\n\r\n"
@@ -1934,7 +1946,7 @@ func (c *conn) serve(ctx context.Context) {
 			}
 			return
 		}
-		c.setState(c.rwc, StateIdle)
+		c.setState(c.rwc, StateIdle, runHooks)
 		c.curReq.Store((*response)(nil))
 
 		if !w.conn.server.doKeepAlives() {
@@ -2965,7 +2977,7 @@ func (srv *Server) Serve(l net.Listener) error {
 		}
 		tempDelay = 0
 		c := srv.newConn(rw)
-		c.setState(c.rwc, StateNew) // before Serve can return
+		c.setState(c.rwc, StateNew, runHooks) // before Serve can return
 		go c.serve(connCtx)
 	}
 }