The npower Championship side were good value for their 2-0 lead thanks to goals from Lee Chung-yong and Marvin Sordell.
However, in the last 30 minutes the Black Cats produced a response which had been conspicuous by its absence in the previous hour as substitute Connor Wickham and Craig Gardner forced a replay.
Bolton stunned their more illustrious visitors by converting their first chance.
With the ball moved to the left of Sunderland's defence, goalkeeper Simon Mignolet had shuffled across to offer an outlet, but when Carlos Cuellar inexplicably squared the ball across the edge of the penalty area straight to Lee, the Belgian was out of position. Bolton's South Korea international wasted no time in sweeping home a first-time shot.
Home goalkeeper Andy Lonergan had a lucky escape when he punched a Sebastian Larsson corner on to the head of Darren Pratley and could only watch it rebounded over the crossbar, but he did better to turn away Adam Johnson's inswinging free-kick.
Three minutes after the interval Sordell added the second from a poorly-defended corner.
Lee's cross was nodded goalward by the unchallenged Keith Andrews and the England Under-21 international headed the ball into the corner of the net for only his second goal since arriving last January from Watford.
The visitors hit back when Steven Fletcher's effort looked set to creep under the crossbar and, although Lonergan did well to keep it out, he was powerless to prevent substitute Wickham firing home at the far post from the resulting corner.
Lonergan, scrambling across his line, kept out yet another Fletcher header as the visitors piled on the pressure and they drew level 15 minutes from time when Gardner fired home a trademark long-range effort.