Former Villa player Barry Bannan almost opened the scoring against his old club but saw home keeper Brad Guzan push his shot onto the post.
But Palace were not to be denied and substitute Dwight Gayle struck in stoppage-time to hand the Eagles their second success on their travels.
The win lifts Pulis' side out of the drop zone on goal difference and the Palace boss hailed a great win after his side had tamely lost 3-0 at home to Newcastle last time.
He told Sky Sports: "Really we needed that result because we'd let ourselves down with the home performance against Newcastle last week so it was nice to bounce back.
"I think we had the more clear-cut chances and the better opportunities and the keeper's made a wonderful save off Bannan - how he touches that onto the post, I don't know.
"But the lads kept going and, like I say, that's what we need to do - week in, week out, we've got to give it everything and they've done that so far."
Pulis has now earned nine points from six games in charge since taking over from Ian Holloway and he believes the organisation of the team is paying off.
He added: "We've worked very, very hard on the shape of the team, on making sure that people are in certain positions at certain times and that everybody knows what they're supposed to do.
"And from that, with the two wide players who've got so much pace and power, we then can cause teams problems.
"But it's very, very important when you work at this level that the team knows what it's doing."