Bolton twice squandered the lead, but Lee Chung-yong secured the victory with a 90th-minute header after drifting into the penalty area to meet Kevin Davies' headed cross.
A fierce shot for a goal by Bolton's Johan Elmander's was offset by Cameron Jerome's score before halftime. Davies restored Bolton's lead with a penalty kick, but Kevin Phillips hooked the ball over goalkeeper Jussi Jaaskelainen to even the score.
In Saturday's other quarterfinal, Manchester United hosts Arsenal. On Sunday, Manchester City plays Reading and West Ham is at Stoke.