The hosts, who were brushed aside 3-0 at the Britannia Stadium two weeks ago, went into the game defending a 12-game unbeaten record in Europe at Bloomfield Stadium stretching back to 2004. Stoke broke the deadlock through Dean Whitehead in the 51st minute, with substitute Peter Crouch tapping in the midfielder's cross 13 minutes later.
Maccabi grabbed a late consolation through Roberto Colautti but Pulis was in no doubt the Potters deserved their victory. The Welshman said: "I thought the lads were brilliant. The balance looked good. The three centre-halves were very solid. There was a bit of a lapse at the end but that's a little bit of tiredness I think."
He added: "I'm very pleased. They huffed and puffed a little bit but I thought we coped with it smashing."
Pulis made nine changes from the side that lost 3-1 to Newcastle at the Britannia Stadium, some enforced while he took the chance to give a number of others a much-needed rest.
It was still a strong side, though, with the likes of Whitehead, Matthew Upson, Thomas Sorensen, Kenwyne Jones and Robert Huth coming in along with Danny Higginbotham, playing his first game for seven months after recovering from a cruciate ligament injury.
Pulis said: "I told him about two weeks ago that this was the game I was looking at and to get himself ready for it. He was smashing before he tired at the end with one or two others as well. Wilson (Palacios) got another 65 minutes. He still isn't as sharp as we want him to be but he needs to play games to get that. It's all great experience for the lads."
The Potters could have qualified on the night had Dynamo Kiev beaten Besiktas in Istanbul but the Turkish team prevailed 1-0, meaning Pulis' side need one point from their remaining two games.
The first of those is a home clash with Kiev on December 1, and the Stoke boss said: "Kiev at the Britannia now is a cup final. If we win the game, we'll win the group, and if we don't get beaten, we'll go through, it's as simple as that.
"It's a massive game for us and I'm sure it'll be a great night because they are a good side. I think it's the toughest group so, if we do it, it's a big achievement, but we still have to do it."
Source: PA
Source: PA