David Weir and Tim Cahill netted either side of the break for the Toffees, sandwiching Shola Ameobi's ridiculous red card for throwing a punch at Cahill.
The win for David Moyes' side means Liverpool can now only overhaul them on goal difference and so he stuck to the team that earned Everton their last league triumph against Manchester United last month.
Cahill passed a late fitness test on a back injury, but Leon Osman missed out. Alan Stubbs returned to the bench after injuring his shoulder last month.
For the visitors, who ended a torrid spell of league form with a hard-earned win at Fulham in midweek, Jermaine Jenas and Celestine Babayaro returned from injury.
But Alan Shearer somewhat surprisingly failed to regain his place in the starting line-up after being rested for the trip to Craven Cottage.
A crescendo of noise welcomed the two teams, the Toffees faithful knowing with Liverpool not playing until Sunday, that this was their chance to all but sew-up that coveted fourth place after a stuttering second-half of the season.
They almost had one foot in next season's Champions League as a brilliant curled free-kick from Mikel Arteta forced a spectacular diving save from Shay Given in the Newcastle goal.
Everton outworked the visitors early on and for sheer fight and determination, troubled Newcastle looked outmatched.
But Graeme Souness' wounded troops almost took the lead after 18 minutes when Darren Ambrose broke clear, but a terrible first touch meant Nigel Martyn was able to gather easily.
Cahill had a golden opportunity to break the deadlock after 21 minutes when another fine floated cross from Arteta found the Australian unmarked, but he could only direct his header straight at Given.
As the game finally settled into a rhythm, Everton settled into their season long hoof it to Marcus Bent tactics whereas the Geordies tried, but failed with their patient passing ploys.
It was the footballing team who pressed towards the end of the half with Patrick Kluivert heading a glorious chance wide, Weir producing a magnificent block from Ambrose and the impressive James Milner forcing a great save from Martyn.
But for all Newcastle's pressure it was Everton who struck first two minutes before the break. A foul from Jean-Alain Boumsong on Bent gave the dangerous Arteta another chance to bend the ball in and Weir was on-hand to nod home, unmarked at the back post.
Eleven minutes into the second period Newcastle once against pressed the self-destruct button as Ameobi swung a punch at Cahill and was dismissed. Idiotic stuff from the former England Under-21 star, who looked dangerous throughout.
Three minutes later Everton doubled their lead as the ever-influential Cahill intercepted a wayward shot from Arteta and smashed it beyond Given.
Everton coasted through the rest of the half safe in the knowledge that regardless of other results they can secure qualification for the Champions League with a point from their last two games.
But with those last two games against high-flying Bolton and second-place seeking Arsenal, the chasing Champions League finalists Liverpool, and indeed Bolton themselves will not be throwing in the towel just yet.
Man of the Match: Mikel Arteta
The Spanish playmaker had a hand in both goals and posed a constant threat to the Newcastle defence with his incisive passing and dangerous set-piece delivery.