Midway through the first-half, the midfielder picked up the ball in front of his own penalty area and turned on the burners, blasting forward and rejecting the chance to release team mate Romelu Lukaku.
Instead he cut in from the right wing, saw Fabricio Coloccini slip and danced to the left of the penalty area before hammering into the roof of the net from the edge of the six-yard box.
Everton had control of the game for long periods tonight and sealed the points with a second after 51 minutes.
On-loan Lukaku, who Newcastle also wanted to borrow from Chelsea in the summer, netted from close range.
The damage was done down the right wing by the probing of on-loan Barcelona winger Gerard Deulofeu. He gave young left-back Paul Dummett a terrible time and tormented him several times on the dribble before setting up Lukaku, who has now scored four goals in four Premier League appearances against Newcastle.
Leon Osman completed the rout late on.
Deulofeu jinked inside the box, laid back to Lukaku who teed up the midfielder to hammer home.