The hosts opened the scoring after a catastrophic error from Carlos Cuellar gifted Chung-Yong lee the opener on 12 minutes, before Marvin Sordell doubled their lead minutes after the break.
However, Sunderland had Connor Wickham to thank for pulling a goal back on the hour mark, before Craig Gardner fired in a long-range equalizer 15 minutes later.
Responding to Bolton’s 1-0 New Years Day defeat at Leeds, Dougie Freedman restored David N’Gog to the starting lineup in place of Kevin Davies, while keeper Adam Bodgan was replaced by Adam Lonergan and midfielder Jay Spearing also dropped to the bench.
Sunderland boss Martin O’Neill, meanwhile, was without defenders John O'Shea, Wes Brown and skipper Lee Cattermole, but selected an otherwise full-strength side in his bid to give Sunderland a fourth straight win at the Reebok Stadium.
And the omens looked good for the Black Cats early on; Bolton hadn’t won in eight previous meetings against them, while Danny Rose and Aaron McClean began by linking up effectively down the left-hand side.
But the home side quickly shattered Sunderland’s game plan as Chung-Yong Lee pounced on a horrendous pass across his own box from Cuellar to drill home his shot and put Bolton 1-0 up.
The visitors looked shell-shocked but soon established a foothold, although Danny Rose was forced off after pulling a hamstring and was replaced by Jack Colback.
Not for the first time this season, it was the Sunderland wide men who caused the most problems, with McClean making run after run and Adam Johnson coming close with an in-swinging free-kick on the half-hour mark.
Lonergan did well to tip the ball wide but it did not stop Johnson persisting, with the England winger shooting wide again shortly after.
But the visitors could not force an equalizer before half-time and looked more at risk of conceding a second when Titus Bramble ran into Mignolet after 40 minutes before finally heading the ball out for a corner.
And shortly after the break, the visitors failed to clear a corner and Sordell was given space to convert from close-range.
Steven Fletcher led a quick-fire response but was first denied by a fantastic save from Lonergan and then by the referee when he was brought down in the box, appealing for a penalty.
However, the introduction of Wickham soon after swung the pendulum back in Sunderland’s favor and sparked the away side into action.
The 19-year-old pulled Sunderland right back into the tie on the hour mark, beating Lonergan from close-range to make it 2-1.
And 15 minutes later, Bolton failed to clear its lines and Gardner was there to punish them, unleashing a fantastic strike from range that had Lonergan beaten from the moment it left his boot.
It was all Sunderland from thereon in and the visitors almost snatched a winner, but ultimately had to settle for a replay at the Stadium of Light.