Adam Johnson's first-half tap-in inflicted a fifth straight away defeat in all competitions on Mark Hughes' men, who had Steven N'Zonzi sent off in the second half for a second bookable offence.
It could have been even better for Sunderland, who spurned several chances to extend their lead, with Jozy Altidore missing the best opportunity, but one goal proved to be enough.
The result sees the hosts move to 17th, while Stoke are just three points above the drop zone in 16th.
Sunderland predictably named a much-changed team from Saturday's FA Cup win over Kidderminster Harriers, but there was no place for midfielder Lee Cattermole as speculation mounts that he could be poised for a move to Stoke.
The visitors handed a debut to Peter Odemwingie, who completed his switch from Cardiff City on Tuesday.
Gus Poyet's side were on the front foot from the off and they had the first sight of goal on seven minutes when Fabio Borini surged forward and laid the ball into the path of Sebastian Larsson, whose shot stung the palms of Asmir Begovic.
That positive start was rewarded with the opening goal 17 minutes in. Borini's tame effort from 20 yards was spilled by Begovic, and Johnson was on hand to tap home the rebound from a tight angle.
After a sluggish opening, Stoke grew into the game and Geoff Cameron should have done better in the 36th minute when he headed over at the back-post from Charlie Adam's corner.
Soon afterwards, Vito Mannone kept the scores level when Adam's cross-shot was met by the head of Ryan Shawcross, who drew a superb point-blank save from the goalkeeper.
Stoke continued to press in the second half but they were reduced to 10 men on 53 minutes. Altidore broke free of the defence only to be tugged down by N'Zonzi, who had already been booked for a challenge on the same man in the first half.
Altidore could have made the numerical advantage pay immediate dividends when the ball broke for him in the box, but he was thwarted by the legs of Begovic.
Sunderland had further chances, with Johnson curling wide from the right-hand side of the box, and Larsson testing Begovic from 25 yards.
Odemwingie almost made them pay for their profligacy when he had the chance to level after 73 minutes, as a neat turn saw him go one-on-one with Mannone, but his weak effort was easily saved.
Stoke came even closer with time running out, Shawcross this time almost earning a point when he guided a lofted header onto the crossbar.
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