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, of course, were a Premier League side themselves only eight months ago, but after a tough time in the second tier found themselves separated from their opponents, struggling in the top flight, by 22 league places.
Many of the players are still on Premier League wages and in the opening 45 minutes it could have been argued they looked the higher-placed team.
Sunderland manager Martin O'Neill named his strongest-possible side, although as if to make a point about the lack of depth in his squad he chose to select only six substitutes.
But after a toothless display in a 3-0 defeat at Liverpool on Wednesday, they looked like offering up more of the same, having been stunned by Wanderers' 12th-minute opener.
Bolton stunned their more illustrious visitors by converting their first chance.
Although it was handed to them on a plate by a defensive error, Lee's casual-looking finish belied a coolness in the heat of the moment.
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 rebounded over the crossbar, but he did better to turn away Adam Johnson's inswinging free-kick.
Sunderland's communication at the back did not improve and there was a distinct air of embarrassment when Titus Bramble and Mignolet got in each others' way and ended up needlessly conceding a corner.
The loss of young right-back Joe Riley to injury strangely helped Bolton's cause as replacement Tyrone Mears provided more of an attacking thrust to put out-of-place Colback under pressure.
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 O'Neill's side will have been relieved just to take the tie back to the Stadium of Light.
- Sports & Recreation