Beattie, 31, scored his fifth goal in seven games following his move from Sheffield United as the Potters eased their Premier League relegation fears at the Britannia Stadium
Substitute Ricardo Fuller made the points safe as Stoke moved up to 15th.
Pulis said: "Players of Beattie's age sometimes need the challenge of proving they can still play in the top flight.
"It was one of the reasons why we went and got him. He wanted this chance.
"His goalscoring record is smashing. Not only that, it is what he does around the place as well.
"He is a very good team man; he gets the players together. He has brought something else to the dressing room. He is a larger-than-life character."
Beattie opened the scoring in the 14th minute. But Bolton hit back, and goalkeeper Thomas Sorensen made a string of good stops before Fuller settled matters 17 minutes from time.
Pulis said: "We needed a performance from Thomas, because he let the first one in at Aston Villa (at the weekend).
"But he has been smashing all season. We defended for our lives. It was a great result.
"It was hard game, a tight game. Credit to Bolton - they never stop. They make it very difficult. But we deserved it, considering the chances we created."
Bolton manager Gary Megson was disappointed with the manner of the defeat and the way the opening goal came about.
He said: "You won't see a worst one conceded up and down the country, never mind in the Premier League.
"Most of the time when the first goal goes in it completely changes the game.
"I thought we had more possession than ordinarily we do have but we weren't good enough with it. We did not compete with Stoke when they were putting balls into the box.
"We did not have all 11 players performing at the level they are capable of and that has cost us."