Teenage sensation Wayne Rooney came off the substitute's bench and set the game alight with his first goals for the Toffees.
The 16-year-old showed tremendous flair and transformed the game after replacing Tomasz Radzinski just after the hour.
Kevin Campbell had given Everton the lead midway through the first half, firing a left-foot angled shot past keeper Paul Whitfield after being set up by Li Tie.
Wrexham had contained their lofty opponents for the greater part of the game but Rooney found space to add a superb second goal.
Duncan Ferguson, playing for the last part of the match as a substitute flicked the ball through and Rooney was on it like a flash to round the keeper and blast his shot home.
The game was stopped for three minutes in the closing stages when supporters wearing Everton colours ran on to the pitch from the Wrexham terrace and raced to the opposite end of the ground.
Some were brought down by police with rugby tackles but others vaulted the low fence and disappeared into the visitors stand.
When play resumed Rooney scored his second goal with ease, racing on to a poor pass from Wrexham's Carlos Edwards, moving on a few yards and finishing with a sublime shot.
Later the Everton youngster dribbled through again and this time Whitfield spread himself and turned the shot away for a corner.
Everton had gone close to scoring early on when Scot Gemmill's header from Tony Hibbert's cross bounced down off the crossbar and was scrambled away by Darren Ferguson.
Wrexham's best chance fell to their top scorer Andy Morrell who saw his short-range header clutched to safety by Richard Wright.
Lee Trundle, a second-half substitute for Hector Sam thundered a late shot against the crossbar.
Wrexham manager Denis Smith said after the match: "We didn't deserve to be beaten 3-0.
"We needed a break in the game but they defended very well and we were always chasing the game after they scored."
Meanwhile David Moyes was pleased with the scoreline and speaking of Rooney he said: "I was delighted to see him score his first goals for the club at senior level.
"He's been a bit anxious about not getting on the scoresheet so this will help him. But Wrexham played well and deserved credit."