Goals from Emanuele Giaccherini and Valentin Roberge were enough to see the Black Cats through to the fourth round as they dominated on a wet Wearside Tuesday evening.
Where disorganisation and fear of failure had crippled the sacked Paolo Di Canio's team, caretaker maanger Kevin Ball's men played with confidence and at times, even a swagger, albeit against more modest opposition than they faced in all but one of the Italian's 13 games at the helm.
Sunderland were in the ascendancy from the off as Lee Cattermole and Giaccherini pressed the Black Cats up field.
Sebastian Larsson fired wide from distance with six minutes gone and Posh keeper Bobby Olejnik had to block Altidore's first-time shot after Giaccherini had played him in.
The Italy international was a central figure throughout the first half, firing wide from a tight angle with 25 minutes gone and then failing to make the most of Jack Colback's cross in front of goal seconds later.
However, it was Giaccherini who eventually made the breakthrough 13 minutes before half-time when he timed his run to perfection to meet Cattermole's inviting cross and half-volley home from close range.
Giaccherini was mobbed by all his outfield team-mates in a show of unity which said much about the prevailing atmosphere in the dressing room.
Altidore rattled a post with a 44th-minute drive as Sunderland negotiated the first half in relative comfort with Danny Swanson the only man to test Keiren Westwood in the home goal.
Peterborough returned determined to force their way back into the game, but Giaccherini saw a shot blocked by Jack Payne and Johnson curled a left-foot effort just wide with Olejnik at full-stretch.
However, it was Westwood who was called into action with 22 minutes remaining when he needed two attempts to claim striker Britt Assombalonga's skidding shot.
But victory was secured 17 minutes from time when, after a left-wing corner had been cleared, Adam Johnson provided an excellent cross for Roberge to head home.