Dwight Gayle and Stuart O'Keefe secured the victory for Palace in the second half after Steven Fletcher had cancelled out Danny Gabbidon's ninth-minute opener.
Gayle scored a late penalty after being brought down by John O’Shea, who was subsequently dismissed, before O’Keefe took advantage of his side's numerical superiority to seal the win in stoppage time.
And Holloway later declared himself proud of his team after they reacted well to being brought level just after the hour mark.
"All you can do is work on your performances, whether you win or not in this division," he said. "The first one we got one or two things wrong against Tottenham, kept giving the ball away, we got better by the end but we lost.
"In the second one we were terrific in the first half, then had a terrible wobble, let a goal in then let another one in. Today, they scored and we didn’t wobble.
"I thought that was a commanding performance. I was so pleased. I’m very, very pleased with the determination, the work rate and the performance. Some of that passing was really nice to watch."
Palace face Manchester United at Old Trafford on September 14 in their next Premier League outing.
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