It was Everton's first home league win since November and eased some of the scrutiny on manager Roberto Martinez in his 100th Premier League game in charge, while ramping up the pressure on Newcastle counterpart Steve McClaren.
A first-half goal from Aaron Lennon, the first time since August 2009 he has scored in back-to-back games, and two late Ross Barkley penalties secured a 3-0 victory against a disparate visiting side who lacked cohesion and Sky Bet offer even-money that Newcastle are plying their trade in the Championship next season.
That price puts them in with Aston Villa (1/66) and Sunderland (1/5) to make the most likely trio in the eyes of the online firm, who eased Norwich to 6/5 on the back of the Newcastle result.
"Although Swansea, West Brom and even Bournemouth aren't out of the woods yet, we say it's any three from four in terms of the relegation dogfight," said Sky Bet's Sandro Di Michele.
"Some firms reckon Norwich are more likely than Newcastle but with trips to Chelsea, Stoke and Leicester coming up soon, we're of the view that the Magpies are in grave danger."