Dwight Gayle secured all three points for Palace at Villa Park on Thursday with a 92nd-minute goal after Villa goalkeeper Brad Guzan had earlier frustrated the visitors with a superb save to tip a Barry Bannan shot on to the post to keep the deadlock intact.
A second away win of the Premier League season means Palace have collected nine points from six games since Pulis succeeded Ian Holloway at Selhurst Park and the result moved the London club out of the regelation zone, above Fulham on goal difference, for the first time since September.
And Pulis was delighted with Palace's resolve following the 3-0 home defeat against Newcastle United on Saturday.
"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," Pulis told Sky Sports.
"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 on to 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."
Since taking charge, Pulis has afforded more playing time to wingers Jason Puncheon and Yannick Bolasie and endeavoured to ensure every player knows their role within the system.
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."
