Hull duo Abel Hernandez and Mohamed Diame scored on their debuts but West Ham equalized through an own goal by Curties Davies to secure a 2-2 draw in the Premier League on Monday.
Hull led twice after the club's record signing Hernandez scored with an impeccable first-half header and Diame restored the advantage against the side he left on transfer deadline day.
In between, Enner Valencia marked his first league start with a spectacular strike from 25 yards and the draw was settled when Diafra Sakho's modest shot evaded goalkeeper Allan McGregor, only for Davies to bundle over his own line.
Valencia almost won it in added time when his header rebounded off Dawson's shoulder and rattled the crossbar.
Hull has five points from four games, with West Ham a point behind.