Aaron Lennon scored and Ross Barkley converted from the penalty spot twice in Wednesday night's Premier League clash against 10-man Newcastle United to seal a 3-0 victory and end Everton's five-game winless run in the top flight.
Things went from bad to worse for Newcastle as they conceded three goals and lost Jamaal Lascelles to a red card in the 93rd minute at Goodison Park.
The midfielder collected the ball off Romelu Lukaku before going for goal, but the Newcastle keeper was quick to react and parried the ball away.
After that attempt, there was a lull in the game, with neither side posing much of a threat until Everton ramped up the pressure on home turf.
The breakthrough was finally made in the 23rd minute when some build-up play ended in Cleverley teeing the ball up to Lennon, who drilled the ball into the bottom left corner from the edge of the box.
Almost instantly, Newcastle came close to responding when Townsend looped a cross into the box and Ramiro Funes Mori fluffed his clearance, allowing the ball to drop to Georginio Wijnaldum's feet, but the forward was flagged offside.
The visitors' first real chance came when none of the Everton players managed to clear a long ball and it fell to Paul Dummett, whose volley went well wide.
Ross Barkley got more involved as the game went on and he almost capitalised on a blunder from Elliot, who lost the ball after opting to head it clear as opposed to catching it, but the midfielder missed the target.
The England international almost produced a second strike before the half-time whistle when he dodged past two defenders and squared the ball across the face of goal, but none of his teammates was there to deliver a simple tap-in.
Newcastle struggled to show much threat in the first 45 minutes, but they defended well at times, particularly Fabricio Coloccini, who dived in to stop Lennon from unleashing a shot from inside the box.
After the break, Everton came out firing and substitute Arouna Kone, who replaced Lukaku at half time, came close to scoring when a rebound off Lennon's shot fell to his feet, but the striker's close-range attempt flew over the bar.
Barkley played a role in the majority of Everton's attacks, one of which would have been a spectacular curling effort had it not been for the sharp reflexes of Elliot.
The Newcastle goalkeeper performed well and he also prevented Cleverley's free kick from nestling into the bottom left corner by tipping the ball on to the post.
Jonjo Shelvey almost scored an embarrassing own goal when he inadvertently headed the ball towards the net off Cleverley's cross, but he was fortunate that the ball bounced off the bar.
The visiting side put Everton under pressure in the closing stages of the encounter, but they did not have enough to get that all-important goal.
The double blow to the Magpies came when Everton were awarded a penalty in the 87th minute after Aarons brought down Lennon in the box.
Barkley was rewarded for his work ethic as he stepped up and sent Elliot the wrong way by nestling the ball into the bottom left corner.
The England international slotted home from the spot kick for a second time when Lascelles brought the midfielder down in the area deep into stoppage time and was immediately given his marching orders.
In the end, it was a convincing win for the Merseyside outfit, who were rarely troubled throughout the game.