The visitors trailed at Goodison Park as Romelu Lukaku capped Everton's impressive start with a goal in the ninth minute.
After finding themselves under concerted pressure in the opening 20 minutes, Palace gradually got a foothold in the game and were level on the half-hour mark when Mile Jedinak clinically converted a penalty after Tim Howard had brought down James McArthur.
Fraizer Campbell and Yannick Bolasie put Palace two goals ahead in the second half and Warnock's men had to hold on in the final stages following Leighton Baines' late penalty.
It was Palace's second successive 3-2 victory at Goodison Park, having won by the same scoreline in April.
"We've done ever so well," Warnock was quoted as saying by BBC Sport. "We should have won the games we've drawn as well.
"Everton are a good side but we've shown great character. You are going to get nervy moments when you play against the quality that they have but I don't think Julian Speroni had too much to do.
"They have listened and I am very proud of them. A win gives everyone a lift and bit of confidence.
"There are not many more difficult places than Everton to go. But we deserved it."
The result lifted Palace out of the relegation zone and up to 15th.
