The young striker, who represented Great Britain at the London 2012 Olympic Games, was at the double to seal the Trotters' progression in a poor game overall on Wearside
In a game desperately lacking in quality and clear-cut chances, the Trotters opened the scoring in the second half from Marvin Sordell's penalty, while the forward bundled home soon after to seal the tie.
Martin O'Neill made three changes to his side that beat West ham 3-0 at the weekend as Matt Kilgallon, Phil Bardsley and Connor Wickham came in for John O'Shea, Sebastian Larsson and Steven Fletcher. Dougie Freedman made six alterations to the line-up that drew 1-1 with Millwall on Saturday.
The Black Cats dominated the opening stages, with Craig Gardner's 20-yard effort curling over before Adam Johnson darted into the box and drew a smart save from Andy Lonergan in the Trotters goal.
Johnson was growing into the match and had the Trotters tied up in knots on the half-hour as he twisted and turned his way into the box, but his cut-back for Wickham was smartly clipped away by Jay Spearing.
Bolton's first real chance came through Chris Eagles' effort that curled wide from the edge of the box soon after, but this stirred a late rally from the Black Cats.
Johnson's 30-yard free kick was neatly tipped behind by Lonergan and, after the Trotters failed to clear the resulting corner, Stephane Sessegnon cut the ball to Titus Bramble, but the defender could only scuff wide with his left foot, while Connor Wickham headed straight at Lonergan from James McClean's cross.
The second-half began in a turgid fashion, but the deadlock was finally broken by Bolton just after the hour, in controversial circumstances.
Darren Pratley burst into the penalty area, before Jack Colback slid in to put the ball behind for a corner, although Kevin Friend adjudged the challenge a foul and gave a penalty that Sordell drilled down the middle of goal.
The game was over as a contest just eight minutes later as Eagles and Tyrone Mears combined on the right, before the full-back's cross resulted in a scruffy melee in the six-yard box, that saw the ball fall to Sordell who prodded home his second.
The goal came as a killer-blow to the Black Cats and the game was played out in a half-paced manner as Freedman's side secured a fourth-round date with Everton.