A much-changed Sunderland side only came to life in the closing stages of the game, and by that point, they were trailing 2-0 to their League One opponents after Simon Mignolet had fumbled Craig Westcarr's fifth-minute flick into his own net before 34-year-old Lee Hughes struck with 15 minutes remaining.
Darren Bent's 81st-minute penalty kept the tie alive until the final whistle, but County held out to claim a famous victory which was little more than they deserved.
Steve Bruce made wholesale changes, admittedly some of them enforced, with one eye on next Sunday's derby clash with arch-rivals Newcastle, but the ploy backfired spectacularly as his side slipped to an embarrassing defeat against the side which also provided the opposition in the third round when they won the cup in 1973.
The after-effects of a gruelling Christmas schedule and the demands of next weekend's revenge mission prompted Bruce into a major reshuffle, but he remained confident there was enough quality in his team to get the job done.
But he was sadly mistaken as his stand-ins failed to live up to their billing.
Despite making seven changes as he rested keeper Craig Gordon, defenders Phil Bardsley and Titus Bramble and midfielders Jordan Henderson and Ahmed Elmohamady, Bruce still fielded a £23million strike-force in Asamoah Gyan and Bent.
However, it was a measure of how poorly Sunderland played before the break that it was not until the last minute of the first half that either managed a shot, and even them, £13million-plus man Gyan scuffed it wastefully.
The Black Cats were able to create little as a midfield featuring Andy Reid and Jack Colback following their return from loan spells was effectively shackled by Ince's hard-working quartet.
But it was at the back where the Premier League side proved least effective, and spectacularly so with just five minutes gone.
Ben Davies' left-wing cross was flicked on by Westcarr and it looked innocuous enough as Mignolet rose to claim it with Lee Hughes making his presence felt.
However, for reasons best known to himself, Kieran Richardson got in on the act and succeeded only in colliding with his own keeper.
The pair looked on in horror as the ball spilled from the Belgian's hands and dropped over the line, sparking mass celebrations among the travelling supporters among a crowd of just 17,582 at the Stadium of Light.
Sunderland's response was laboured as Bruce took up residence in his technical area, but they went close to an equaliser with 28 minutes gone.
Reid embarked upon a powerful run to the edge of the County box and after exchanging passes with Bent, sent a left-foot shot just over the angle of bar and post.
But the Wearsiders' fragility in defence almost cost them once again two minutes later when Magpies skipper Mike Edwards was allowed to meet Davies' free-kick beyond the far post and send a left-foot shot across goal and just wide of the far post.
Westcarr might have double his tally with four minutes of the half remaining when he curled a right-foot effort towards the bottom corner, but Mignolet made amends for his earlier error with a good save to spare his side further damage.
Gyan should have sent his side in at the break level after Reid forced a pass through to him, but he mishit his shot as keeper Stuart Nelson came to meet him and Krystian Pearce was able to head clear.
Sunderland's response to whatever Bruce said at the break was distinctly lukewarm in the early stages of the second half, and Bruce made his move on the hour when he withdrew Cristian Riveros and Colback and sent on Henderson and Elmohamady.
The newcomers combined to great effect within two minutes for the Egyptian to set up Steed Malbranque, but he sliced his shot horribly wide.
Bent headed wide from a 64th-minute Elmohamady cross and then again from a Richardson's delivery eight minutes later with the Black Cats belatedly building up a head of steam.
But their hopes were dashed 15 minutes from time when Hughes skipped through a flat-footed defence and despite seeing his initial shot saved by Mignolet, thumped the loose ball into the empty net from a tight angle.
Bent gave Sunderland hope when he claimed his 11th goal of the season from the penalty spot after Richard Ravenhill had tripped Reid with nine minutes remaining and then headed over in the sixth minute of injury time, but there was to be no late rescue act.