The Championship side looked to be in control of the third round clash as dismal defending allowed Lee Chung-yong to open the scoring in the 12th minute before Marvin Sordell took advantage of more shoddy play at the back to double their lead early in the second period.
But the introduction of striker Connor Wickham swung the tie back towards the Premier League outfit as he levelled on the hour mark before Craig Gardner drilled home a superb equaliser from outside the box with 15 minutes to go.
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. It would be an over-statement to suggest the goal sparked the Black Cats into life, but they at least began to exert some influence on a game which had hitherto passed them by. They were not helped by the loss of left-back Danny Rose to a hamstring injury, which forced midfielder Jack Colback to come on in his place.
David Vaughan's long-range effort was comfortably stopped by second-choice goalkeeper Andy Lonergan, making only his second appearance of the season. Lonergan had a lucky escape when he punched a Sebastian Larsson corner on to the head of Darren Pratley and could only watch it rebound over the crossbar, but he did better to turn away Andy Johnson's inswinging free-kick.
Sunderland's top-scorer Steven Fletcher was having one of those days and headed a corner over just before half-time. It was to prove costly as 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 for £3million.
Seconds later Lonergan belied his lack of activity this season, brilliantly throwing up an arm to deny Fletcher's close-range diving header. However, another Fletcher header - and he had many throughout the afternoon - led to the visitors pulling one back on the hour.
The Scotland international'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.
Sunderland's aerial superiority was something they had not taken advantage of all afternoon, but Wickham's arrival gave them another target to hit, although when he headed back across an open goal there was no team-mate available to convert.
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. The visitors pushed for a winner late on, but in truth Martin O'Neill's side will have been relieved just to take the tie back to the Stadium of Light.