Papiss Cisse gave the visitors the lead two minutes after half-time and it looked like Alan Pardew's team would end their miserable run of three straight Barclays Premier League defeats as the game headed into the final 10 minutes.
But in the 81st minute Cameron Jerome crossed for Jonathan Walters to head in, and four minutes later two substitutes combined as Kenwyne Jones set up Jerome for the winner.
Stoke had huffed and puffed without really looking like getting back into the game until Pulis introduced Jerome and Michael Kightly midway through the second half, but he insisted the credit should not be directed his way.
The Potters boss said: "I've always got this thing in the back of my mind that when people say, 'Oh, he's made changes, he's been brilliant,'.
"Why didn't I start with Michael Kightly, why didn't I start with Cameron? That's how brilliant I am.
"The lads have been fantastic, they've not played much this year but the spirit has been very good and their commitment to the group has been fantastic.
"They could easily have come on tonight and just jogged around and done what they wanted to do for themselves, but the effort they put in for the team was there for everybody to see, and that is a real plus for their character. And I think that really typifies what we've got at the football club."
The Britannia Stadium had only seen six goals in as many games prior to Wednesday and in the first half it was easy to see why, with the closest either side came a miscued Mike Williamson clearance that hit his own post.
But the visitors broke the deadlock immediately after the break, Asmir Begovic spilling Demba Ba's 25-yard shot and Cisse following up with a much-needed goal for himself and his team.
Cisse and Ba both came close to adding to Newcastle's advantage on the break but Stoke kept plugging away and got their reward to climb to ninth in the table.
Pulis said: "I thought the first half was very even. The last three games we've hit the post or the bar in every game and not had a break where it's come out to us or it's come off the inside of the post and gone in.
"So when that happened in the first half, you just think maybe it might not be your night. And when Asmir spills one, and he's been absolutely brilliant this season, and they tap it in, again you think it might not be our night.
"We made the substitutions and that brought a little bit of life into the game. I thought it lifted the crowd as well, and the crowd in the last 20 or 25 minutes were absolutely wonderful.
"When we got the equaliser, the belief in the crowd, you actually think, 'Well, we'll go on and win this'."
The only negative for Stoke was the loss in the first half of Peter Crouch, who was caught in the mouth by a flailing arm from Fabio Coloccini.
Pulis said: "He wanted to carry on until he saw his teeth in the doc's hands, and then he nearly fainted. He'll need some work on that. I haven't seen it (the challenge) but I don't think there was any malice in it."
Newcastle boss Alan Pardew was left feeling his side - who have now lost four straight league games for the first time since 2008, when they were relegated - did not get their just desserts.
He said: "Sometimes you have a game plan and your players see it through to the letter and it's pretty galling to look them in the eye and say they've come away with nothing, which I had to do.
"A couple of mistakes cost us the game, and we didn't make many mistakes. It's a tough result for us to take."
Pardew also felt his side should have had a second-half penalty for handball, but he hopes the improved showing bodes well for future games.
"That's the sort of break you need when you're on a run like ours and we didn't get it," he said of the penalty shout.
"But I look at my team and it was such an improved performance. There was real commitment, a good balance to the team, and, if you're going to get a victory, that's the sort of performance that's going to lead you to one."