Boss Steve Bruce insisted Newcastle must finish their Premier League survival job after Callum Wilson claimed a second-half brace in a stunning 4-2 win at Leicester.
Wilson's double added to first-half goals from Joe Willock and Paul Dummett as the Magpies shocked the Foxes.
Bruce's side will be safe if Fulham drop points against Burnley on Monday as the Cottagers can only match their tally of 39 points.
Marc Albrighton and Kelechi Iheanacho scored two late consolations for the Foxes, who suffered a potentially-damaging blow to their Champions League qualification hopes.
Newcastle climbed to 13th in the table but Bruce promised not to relax in their survival fight.