The Black Cats began life after Paolo Di Canio well, with the former Juventus man and Valentin Roberge both on the scoresheet against their League One opposition
Emanuele Giaccherini's first home goal since joining from Juventus and substitute Valentin Roberge's second-half header sent the Black Cats into the fourth round as they put Sunday's dismissal of Paolo Di Canio firmly behind them.
Kevin Ball, who took charge at the end of the 2005-06 season, was again handed the reins on an interim basis and named a strong side, including Carlos Cuellar, Sebastian Larsson and Lee Cattermole, who started for the first time since February.
The visitors were without suspended duo Nathaniel Knight-Percival and Mark Little following their red cards in Saturday's 2-1 victory over Milton Keynes Dons, whom Sunderland beat in the last round.
Peterborough, who scored 11 goals in the opening two rounds, suffered a further setback inside the opening 10 minutes as forward Lee Tomlin, the competition's top scorer with five strikes, hobbled off following a strong challenge from Ki Sung-Yueng, which earned the Korean a yellow card.
And the midfielder almost rubbed salt in the wound seven minutes later when he headed over the crossbar from inside the six-yard box.
It was the home side who continued to make most of the early running and Giaccherini should have done better after latching onto Jack Colback's searching cross but the Italian looped his effort over the bar.
Peterborough created a rare chance of their own when substitute Joe Newell tried his luck from range, only to see his shot go just wide.
Sunderland got their deserved breakthrough after 32 minutes, though, when Giaccherini fired home Cattermole's cross on the half-volley and they almost doubled their lead on the stroke of half-time, only for Jozy Altidore to be denied by the post.
The game should have been put out of the League One side's reach early in the second half, with Giaccherini and Altidore both failing to capitalise on presentable opportunities.
Peterborough sounded a warning at the other end as Britt Assombalonga, who has eight goals to his name already this season, had the ball taken off his toes by Sunderland goalkeeper Kieren Westwood.
But the home side wrapped up the victory with 17 minutes to go when Frenchman Roberge, who came off the bench in the second half, headed home his first goal for the club after Peterborough failed to deal with a corner.