Bolasie's tireless running helped haul his side back into the game after Romelu Lukaku's ninth-minute opener for the hosts and he capped a fine display by scoring what turned out to be the winner to seal a 3-2 victory.
Mile Jedinak had equalised for Palace from the spot on the half hour and Fraizer Campbell took advantage of a Tim Howard blunder to put his side in front nine minutes after the interval before Bolasie stroked home their third in the 69th minute.
Leighton Baines scored an 82nd minute penalty for Everton to spark a frantic finale but ultimately Roberto Martinez saw his side's recent revival grind to a halt due to individual errors.
Warnock, who brought Bolasie back into his starting line-up in place of Wilfred Zaha, said: "I've seen Yannick for a long time now and he always contributes and is a threat.
"The problem with him is he doesn't know what he's going to do next so the defenders have got no chance
He was very positive today and he covered a lot of ground."
Warnock is still in the process of evaluating his squad after replacing Tony Pulis as manager but believes he has seen enough in his eight games in charge to date to inspire plenty of confidence.
He added: "This gives everyone a lot of belief
We should have won the other two games against Newcastle and Burnley and we were disappointed not to.
"I thought we deserved to win it today
We were apprehensive in the first 20 minutes and gave them a bit too much respect but from that moment we grew into the game and we said it was a game we could go on and try to win.
"What pleased me was that Everton are a good side and we had to hang in there at times and put our head in and make tackles and blocks, and I like that kind of football."
Everton boss Martinez conceded his side were guilty of individual errors as they saw their recent revival brought to a juddering halt.
Howard in particular had a day to forget after giving away the opening penalty then failing to reach a Martin Kelly cross which gifted Campbell Palace's second goal
Leon Osman's mistake then allowed Jason Puncheon to set up Bolasie for Palace's third.
Martinez said: "We wanted to start sharp and to be bright with everything and for the first 15 minutes we looked fresh and scored a very good goal.
"But we didn't really have that drive about us to score a second goal and if we had done so in that period then the game is over.
"The penalty was an incredible reward for Palace and from then on the mental change allowed Palace to have a lot of belief and to change the game.
"It was very uncharacteristic of us to concede three goals with three errors, but even then the character was incredible and we almost managed to get something out of the game."
Everton's busy schedule is set to continue with a Capital One Cup trip to Swansea on Tuesday before next week's Merseyside derby, and Martinez acknowledged the importance of getting back to winning ways.
"It is a really busy period and we want to make sure we take advantage of it," the Spaniard said.
"There is a real competition for places and we need everyone to be ready
Those games are going to be vital to see how well we can progress."
Source : PA
Source: PA