Zan Vipotnik's 17th Championship goal of the season and a brilliant long-range effort from Liam Cullen proved enough as Swansea beat 10-man Stoke 2-0 at the Swansea.com Stadium.
Vipotnik - the division's leading scorer - glanced home a header from a corner in the 53rd minute after Wales international Sorba Thomas had received a second yellow card in the first half.
Thomas was dismissed for a shove on Goncalo Franco after 36 minutes, having been booked for a foul 13 minutes earlier.
Vipotnik's goal looked enough to extend Swansea's unbeaten home league record to 10 matches, before Cullen made sure of victory with a spectacular 50-yard effort in stoppage time.
The Wales international was near the halfway line when he spotted Stoke goalkeeper Tommy Simkin off his line, before striking a perfect shot.
Stoke have now won just once in 11 matches in all competitions, although they remain well clear of the relegation zone.
True to their previous healthy home form, Swansea were quickly into their stride and created early opportunities.
Vipotnik fed Ethan Galbraith in the first minute but his shot lacked power and Simkin was able to make a comfortable save.
The Stoke goalkeeper was more severely tested when a neat pass by Jisung Eom gave Josh Tymon the space to drill a low shot that was heading for the far corner until Simkin made the save at full stretch.
It took until midway through the half for Stoke to pose their own threats and they would have taken the lead had Josh Key not blocked a close-range effort from Eric Bocat.
Soon after, Swansea keeper Lawrence Vigouroux made a spectacular diving save to deny Ashley Phillips' header as Stoke pressed hard for an opening.
But they gave away cheap free-kicks and two yellow cards, including one for a foul by Thomas that would prove very costly.
In the 34th minute, Stoke thought they had gone ahead when skipper Ben Wilmot headed home from a corner, but an offside call against Phillips meant the goal was wiped off.
That decision angered Stoke's players and as tempers rose, Thomas pushed Franco which earned the winger a second yellow card.
Replays suggested it was harsh decision as the players were colliding, with Thomas possibly using his hands as protection.
The outcome, though, meant Stoke were reduced to 10 men in the 36th minute.
Swansea were unable to make their advantage tell before half-time, but did not have to work too hard to go ahead after 53 minutes.
Stoke's defenders switched off at a corner from Tymon, enabling Vipotnik to drift away from his markers and glance a header into the far corner.
They might have improved their lead but Franco, Galbraith and Brazilian Ronald all saw their efforts fly wide.
Swansea substitute Gustavo Nunes then seemed to have all the time in the world to fire home a second goal in the 78th minute but the Brazilian dithered and the chance was wasted.
Stoke had one late chance to level before Cullen's beauty, but Bae Jun-ho flashed a volley wide in the 88th minute.
Swansea's Vitor Matos:
"The win was always about how to play with an extra player. I think that's quite important.
"You need to have the right structure, you need to have the right mindset, the right discipline, and we had that.
"The goal gave us a little bit of tranquillity and we kept the momentum for 70 minutes. Stoke reacted but we stayed calm to get the game back under control.
"The bench was really important and when you have Liam you can always score, which he did with a wonderful goal."
Stoke's Mark Robins:
"How can you be penalised for trying to take a shot mid-air and somebody is putting the head down? How?
"Was anybody hurt? No. So, that puts him on a tightrope, but for all the good he's done after that, the second yellow can't happen.
"It's a loss of discipline. Whether it was a kick out or whatever, I don't know.
"The goal that we conceded was really poor but we still carried a threat right up until the end. We need to lick our wounds ready for the game [against Ipswich] on Tuesday."
