Jason Puncheon produced the winner for the hosts.
Despite some late jitters, Pulis felt Palace fully merited victory against his former club, ending the week he turned 56 with a belated birthday gift.
"It's a pleasing result for us, because we need to win home games, and to get a clean sheet was good," said Pulis.
"I was hoping and praying we'd get a second goal but Butland made some great saves.
"I felt more nervous in the last 10 minutes when they pushed Shawcross up front and just played balls into the box.
"You're hoping one of those doesn't drop to someone, luckily it didn't, and fortunately for us.
"We broke ever so well at times, created good opportunities from that and we should have scored more goals."
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