Crystal Palace were let down by a sorry start to the second half as they crumbled to a 3-1 defeat at Goodison Park.
An evenly matched contest looked as if it could swing either way until the break, Everton coming out much better and going ahead with a 46th minute goal from Gylfi Sigurdsson.
Oumar Niasse added another for the hosts less than 10 minutes later, Palace sucker-punched as a result of some poor defending. Tom Davies added a third just over ten minutes from time to seal things before Luka Milivojevic's consolation penalty.
Allardyce gets one over Hodgson
There had been something of a war of words in the press building up to this one, Palace boss Roy Hodgson suggesting that there was bad blood lingering from insulting personal comments made about him by opposite number Sam Allardyce back in 2016.
The two veteran bosses were desperate to get one over the other, both watching their side go close early on.
Gylfi Sigurdsson looked in the mood for one of his better displays at Goodison this season, showcasing his goalscoring intentions with an early shot from distance that dropped just wide.
At the other end, Luka Miivojevic benefitted from some powerful play by debutant Alexander Sorloth, who shook off Eliaquim Mangala to set up the midfielder for a shot that crashed just wide of Jordan Pickford's post.
Wayne Hennessey made a good stop from Idrissa Gueye in the closest we came to a first-half goal, the Welshman diving low to his right to tip Gueye's bouncing effort wide.
Defensive madness does for Palace
After three fans completely fluffed their crossbar challenge attempts at half-time, the crowd thought they'd seen enough comedy around a penalty area for the time being, only for Palace's defence to commit to such acts of foolery for a horror spell at the start of the second-half.
Sigurdsson opened the scoring less than 60 second after the restart.
With Palace defenders Timo Fosu-Mensah and James Tomkins both drawn to the ball, Niasse bundled it to Sigurdsson who took his chance to burst into empty space and fire past Hennessey into the bottom corner.
That buoyed Everton and put the Eagles well and truly on the back-foot, with a second goal coming seven minutes later.
Again Palace's centre-backs were nowhere to be seen as an Everton attacker found space in the area, Niasse left alone as Tomkins and Fosu-Mensah rushed to the ball, the striker making no mistake to head past Hennessey from Cuco Martina's cross.
Two late goals, no late drama
Palace, now two down, did look to fight their way back into the game but couldn't do it through striker Christian Benteke, the Belgian missing a glaring opportunity to halve the deficit as he beat substitute Jonjoe Kenny to Yohan Cabaye's cross.
It was then the turn of Sorloth, who had been played in an unnatural wide-left position, to get an effort at goal as he rose highest in the box from a Patrick van Aanholt ball in, the new signing denied a debut goal by a good Jordan Pickford save.
Palace's missed chances came back to haunt them as Tom Davies' goal ruled out any chance of a comeback. Hennessey thought he'd done enough to prevent Everton from a third as he saved from Sigurdsson, only for the ball to fall kindly to the waiting Davies in the ensuing scramble.
There was time for one more goal as Ashley Williams handled in the box, Milivojevic stepping up to beat Pickford and give the travelling contingent something to cheer, although they'll be quietly worried about their side being winless in four and now just two points from the drop zone.