Steve Clarke's cheap fut coins side were leading through Zoltan Gera's blistering first-half strike when Mignolet allowed the ball to slip from his grasp and Shane Long tapped in to cement Albion's lead.
Craig Gardner got one back for Sunderland in the second half before a penalty from Albion forward Romelu Lukaku. Stephane Sessegnon struck late for the hosts, but Marc-Antoine Fortune sealed the Baggies' fourth successive win in added time.
West Brom's victory lifted the season's surprise package above Chelsea and within two points of leaders Manchester City, while Sunderland lie only three points above the relegation zone.