The south-east London side created the better chances against their Birmingham opponents, with Cameron Jerome denied by a last-ditch Ciaran Clarke clearance.
Marouane Chamakh has come on today and I thought he was different class
The former Stoke City striker hit the crossbar as the Eagles continued to press for a winner against Lambert’s men at Selhurst Park.
And Puncheon netted the decisive strike with 14 minutes remaining as the ex-Southampton forward scored his third goal in two Premier League games.
“We had a slow 20 minutes and we had to shift the ball from one side of the pitch to the other quickly,” Pulis told BBC Sport.
“Jason Puncheon is a cracking lad but they all are. Marouane Chamakh has come on today and I thought he was different class.”
Meanwhile, Villa manager Paul Lambert was left to rue fine margins which denied his side any points.
“It was a really tight game, a physical game, there was nothing much in the game, they took their chance. The game could have went either way,” Lambert said.
It’s a really fine margin in that game today. It is where it is, there’s loads of teams and games still to play and you have to get over that finishing line as quick as you can. We saw a lot of ball and a lot of possession.
“There were wasn’t too many chances for both teams.”
Palace moved up to 12th place and seven points clear of the relegation zone after Saturday’s win.
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