Newcastle goalkeeper Krul could only watch helplessly as Pieters' attempted cross from the left drifted over his head and dropped inside the far post.
It was just the third goal of the 25-year-old's career, and his first since he scored the winner for FC Utrecht against FC Groningen in April 2008.
Pieters and Krul have been friends since playing together for the Dutch Under-17 team, and the full-back joked: "I told him I meant it.
"Everybody knows he's my best friend in football. I've known him since I was 17. It was really good to score my first goal, and a great goal as well, against him.
"We talk to each other a lot, about our personal lives as well. We support each other always and we have a good relationship. I'll keep texting him, for sure."
Pieters still harbours hopes of a World Cup appearance in the summer, has formed a good partnership with winger Marko Arnautovic down the left-hand side, and he said: "I like to play together with Marko.
"We have had to learn how to play with each other and I think we're showing that every week we're getting better and better.
"The team didn't play that well. I know we can play better, but, when you win and keep a clean sheet, that's the most important thing."
It was Stoke's fourth victory from their last five matches and keeps alive their hopes of a first top-10 finish in the Premier League.
Midfielder Stephen Ireland said: "We want these last games to mean something, and we're chasing teams down.
"The manager wants us to win every game between now and the end of the season. He's not going to let us take our foot off the gas whatsoever.
"It was a tough game. We were sloppy, they were sloppy - it was just one of those games. Luckily we got the three points. If anyone was going to win the points, it was us.
"We had 40 points coming into this game and I don't think that's enough to start celebrating. The manager wants 50-plus. That's what he wanted at the start of the season. We're in a position to do it, so we're going to go for it."