Crystal Palace striker Alassane N'Diaye's first senior strike ended Championship leaders West Brom's unbeaten start.N'Diaye cashed in on Albion defender Shelton Martis's error to coolly side-foot past Scott Carson.
Luke Moore was earlier denied by Palace keeper Julian Speroni.
After Palace took the lead Jonas Olsson flashed a header wide and Roman Bednar failed to hit the target from six yards as Albion pushed for an equaliser.
West Brom manager Roberto di Matteo: "It was a very soft goal for us to concede. It was a straight ball into the box and we should be able to defend it better than we did."
"In tight games like that if you get a chance or two we need to be clinical and put them away.
"You will not get too many when teams defend with all their men and it becomes difficult.
"I think every team who comes here does that and we need to cope with that."
Crystal Palace boss Neil Warnock: "This is what we are in the game for. Two weeks ago, the defeat to Scunthorpe was probably the lowest part of my career and this result is one of the highest.
"I thought we were super. Everyone gave me everything. We didn't come to defend, we came to have a go at Albion. We pushed right up on them and I think we deserved the win.
"We had read that this was going to be Albion's ninth game without defeat and I think things like that help you.
"You have to defend for your lives against a team like this who are scoring goals for fun. That is what makes the result so satisfying for me and I am really proud of my lads."