A fine goal from George Honeyman saw Sunderland edge through to the next round of the Caraboa Cup.
In a game which Sunderland dominated without creating enough, the academy graduate linked up with Joel Asoro to settle the contest with an excellent chip.
The Black Cats saw the vast majority of the ball throughout the game, but established attackers such as Aiden McGeady and Wahbi Khazri struggled to open up the Bury defence.
In the end it could and should have been more comfortable, with Didier Ndong blazing over from inside the box with just minutes left to play.
The opening exchanges had raised hopes of a high tempo encounter, Lewis Grabban heading just wide of the near post after a fine cross from Brendan Galloway.
Moments later, Aiden McGeady forced a fine save from former Sunderland goalkeeper Joe Murphy, the winger cutting inside onto his right foot and firing across goal.
Bury began with plenty of endeavor themselves, but struggled to create openings after captain Stephen Dawon was taken off on a stretcher with a serious leg injury.
From there Sunderland dominated possession, with Darron Gibson influential in the heart of midfield. Bury's five man defence left their new look strike force isolated, Tyias Browning able to push up the field and snuff out any attacks at an early stage. The end product was missing for Sunderland, however, with Murphy rarely tested. McGeady delivered some excellent crosses but with James Vaughan on the bench, the movement and presence in the box was missing. Grabban and George Honeyman worked hard but could not create a moment of real quality to open up the opposition defence.
The closest the visitors came was a chance strike from Wahbi Khazri, striking a second ball on the volley from 30 yards. The Tunisian had Murphy back-pedalling but his effort drifted wide.
Grayson introduced James Vaughan at the break, replacing Lewis Grabban.
The Black Cats ought to have gone ahead just five minutes into the half. Khazri, disappointing in the opening period, did well to steal the ball from the Bury defence and had the goal gaping when he went round Murphy. As he went to strike the ball, however, his right leg gave way and he slipped to the ground, a regular occurrence for a number of players throughout the game.
Sunderland continued to threaten without finding a goal, Vaughan twice shooting on target but without the power to really test Murphy.
Substitute Joel Asoro helped break the deadlock, linking up well with Honeyman. One-on-one, the midfielder dinked the ball over the keeper with superb composure to finally give the visitors the lead.
Bury responded by lifting the tempo, Jermaine Beckford firing just wide from distance with Steele scrambling in the Sunderland goal.
The Black Cats almost made sure of the win when Honeyman again fought his way into the box. The ball broke to Asoro but Murphy was quick off his line to make the block, Vaughan chipping over with the follow-up.