diff --git a/src/net/http/h2_bundle.go b/src/net/http/h2_bundle.go
index 29296991ef386c..b03b84d2f30957 100644
--- a/src/net/http/h2_bundle.go
+++ b/src/net/http/h2_bundle.go
@@ -7168,6 +7168,7 @@ func (t *http2Transport) newClientConn(c net.Conn, singleUse bool) (*http2Client
 	cc.inflow.add(http2transportDefaultConnFlow + http2initialWindowSize)
 	cc.bw.Flush()
 	if cc.werr != nil {
+		cc.Close()
 		return nil, cc.werr
 	}
 
@@ -7533,6 +7534,15 @@ func (cc *http2ClientConn) roundTrip(req *Request) (res *Response, gotErrAfterRe
 	bodyWriter := cc.t.getBodyWriterState(cs, body)
 	cs.on100 = bodyWriter.on100
 
+	defer func() {
+		cc.wmu.Lock()
+		werr := cc.werr
+		cc.wmu.Unlock()
+		if werr != nil {
+			cc.Close()
+		}
+	}()
+
 	cc.wmu.Lock()
 	endStream := !hasBody && !hasTrailers
 	werr := cc.writeHeaders(cs.ID, endStream, int(cc.maxFrameSize), hdrs)