The Black Cats, who had scored only twice in five games in all competitions before kick-off, rattled in four unanswered goals against the Potters to claim just their third home win in the Barclays Premier League this calendar year.
Victory eased the pressure on Bruce, who had been the target of intense criticism from disgruntled fans still smarting at the 1-0 home defeat by arch-rivals Newcastle in the second game of the campaign.
The former Manchester United defender chose to send out number two Black to conduct the post-match press conference, and he revealed how tough the last few weeks has been on the manager.
Black said: "It hurts him. People think he is this big, robust character, but it hurts him when he doesn't win.
"He's a winner, he always has been and he will always be that way, so it hurts him when it doesn't go the way he wants it.
"Sometimes, I think the criticism is unfair, I would have to say in my opinion, it is unfair because he works hard and he puts decent teams together.
"But such is life. That's the pressure of managing in the Premier League.
"It's nice to get a victory. Any victory in the Premier League is great, but under the circumstances he has had to deal with personally - because he is from this area as well - I think he will be quite happy tonight."
Sunderland got off to the perfect start as they doubled their season's goals tally within 11 minutes.
Stoke keeper Asmir Begovic may feel he should have done better when he allowed Titus Bramble's fifth-minute shot to squirm from his grasp to hand the defender a first goal for the Black Cats, and Bramble's former Newcastle team-mate Jonathan Woodgate compounded the misery by heading Sebastian Larsson's cross into his own net six minutes later.
Home keeper Simon Mignolet had to make a fine save to keep out Marc Wilson's 16th-minute free-kick, but the game was effectively over when Craig Gardner's 28th-minute shot was deflected past Begovic by Ryan Shawcross.
Larsson added a fourth with a curling 58th-minute free-kick to seal a win which lifted Sunderland out of the bottom three.
Perhaps significantly, Bruce fielded seven of his 11 summer signings from the start as skipper Lee Cattermole was left sitting on the bench, and David Vaughan, Larsson, John O'Shea and Wes Brown in particular stood out.
Black said: "Every team has to build and get new players into the team, but today the quality the manager has signed was there for everybody to see and hopefully, we can maintain that level of performance."
Stoke boss Tony Pulis refused to make his side's midweek trip to Kiev an excuse as he made poignant mention of this week's mining disaster in his native Wales.
He said: "We live in a bubble in football and sometimes you have to burst that bubble and look outside.
"Those poor people have been underground working very, very hard to look after their families. They would earn in a year what some of our players earn in a week, and we cuddle them and mither them maybe too much at times.
"There's no way in a million years that anybody at Stoke City will make excuses for travelling, for them coming back and having bad performances.
"We are very, very unfortunate in some respects that, every time we play in Europe, the next game is away from the Britannia. We are very, very unfortunate and we can't do anything about that.
"But make excuses? After what's happened to those people down in South Wales, which is where I was brought up, no, there are no excuses from this football club for our players."