A brace from Jason Puncheon and former Cardiff midfielder Joe Ledley saw the Eagles cruise to victory and three points closer to Premier League safety.
Victory at the Cardiff City Stadium made it two-in-two for Palace following their 1-0 shock win over Chelsea at Selhurst Park.
Since taking the reins at Palace in November, Pulis has inspired a revolution which has seen the club elevated to 14th in the top flight and Jerome believes the Welshman ranks among the best managers in the Premier League.
"He is definitely up there," the ex-Cardiff striker told the Daily Star.
"Jose Mourinho said last week, from where we were to where we are now speaks for itself.
"It's not necessarily the manager that wins the league who is the best; it's the one who has done the best job.
"I think with the resources he has got, the amount of people that have written him off, Tony has done an unbelievable job."
When Pulis arrived at Selhurst Park, the Eagles had amassed just seven points from their opening 12 matches.
In their subsequent 20 matches, Pulis has inspired eight victories and three draws as Palace have started to distance themselves from the fierce relegation battle.
"He deserves every plaudit that he gets," Jerome claimed.
"He had a point to prove coming here and he's the sort of man who relishes that sort of challenge.
"If he manages to keep us in the Premier League, he will have done a fantastic job. His tactics are spot on."
Jerome believes Pulis is underrated as a manager and insists there is much more to his coaching than meets the eye.
"He knows everything about our opponents and he's just a natural-born winner," he added.
"You can talk about other people being 'The Special One' and this or that, but he doesn't get enough credit for the way he plays.
"People say he's one-dimensional and plays long balls, but he's got Premier League experience. He knows what it takes to stay in this league."