Record signing Asamoah Gyan's double clinched a 2-0 win over the Potters, who had defender Ryan Shawcross sent off late in the second half, although the Black Cats missed a penalty and survived concerted appeals for a spot-kick with the score at 1-0.
The three points moved the Wearsiders back into seventh place in the Premier League, six days after their 5-1 defeat at Newcastle.
Bruce said: "It's been a tough week and the one thing I am pleased about is the young players.
"They were all determined, and they were maybe trying too hard in the first half, to try to make amends if they could.
"In some eyes we have repaired some damage, in some eyes we won't repair it at all.
"But thankfully we showed a bit of bottle, we kept a clean sheet and showed what we are made of a little bit in a really difficult week."
It took Ballon d'Or nominee Gyan just nine minutes of his first league start to make his mark, side-footing into an empty net after goalkeeper Asmir Begovic had parried Nedum Onuoha's shot.
Sunderland should have extended their lead on 28 minutes when they were awarded a penalty for Jon Walters' tug on Gyan's shirt.
However, with leading scorer and penalty taker Darren Bent missing with a hamstring injury, Steed Malbranque saw his spot-kick saved by Begovic.
Stoke gradually fought their way back into the game and were denied the chance to equalise with 19 minutes remaining after Lee Cattermole somehow kept out former team-mate Kenwyne Jones' header on the line.
Replays suggested he had done so with his arm, with some visiting players appealing for the penalty and others claiming the ball had crossed the line, although both claims were waved away by referee Martin Atkinson.
Their woes deepened when Shawcross was sent off for two bookable offences, the first a dreadful challenge on Danny Welbeck, and Gyan blasted home a second four minutes later.
Bruce said: "Thankfully the new striker showed what a class act he is today, I thought he was terrific. He gave us a spark and lift which we needed."
Stoke boss Tony Pulis was furious at the Cattermole decision, and Bruce admitted his men had got away with it.
Pulis said: "The decision was a game-changing decision. That's the sixth in 11 games that we have had given against us.
"It's handball, everybody will agree it's handball, Cattermole gets sent off, you hope you score the penalty and it's then 11 Stoke City players against 10 Sunderland players with 20 minutes to go.
"Shawcross doesn't get sent off and it is a completely different game. It's very, very disappointing.
"You go into games and referees are going to make mistakes, like players do, like every one of us in this room will do. You just hope they don't make game-changing mistakes.
"I have just seen the television replay. I never see the referee, but I will go to see him today. He has actually got a clear view from the camera angle that I have seen."
Pulis also defended Shawcross for the 79th-minute challenge on Welbeck that cost him his first booking.
He said: "People make split-second decisions to make challenges and sometimes they mistime the challenges, you are going to have to accept that.
"I don't think anybody goes out to seriously, seriously hurt another player. Those days are gone."