Steven Pienaar dumped Sunderland deep into relegation trouble as Everton climbed into fifth place in the Premier League table.
The South African midfielder fired the visitors into a 48th-minute lead and then set up Marouane Fellaini to secure the points 19 minutes from time as the Black Cats slumped to their ninth home league defeat of the season.
They remain four points clear of the bottom three with three games to play, but face tough away trips to Bolton and Portsmouth before Chelsea head for the Stadium of Light on the final day of the campaign.
Painfully for Sunderland boss Ricky Sbragia, whose side have now taken just five of the last 30 points they have contested, they were well beaten by an Everton side depleted by injuries, but still too good for them.
The opener came Jo collected Phil Neville's pass with his back to goal and span Anton Ferdinand before sliding the ball into the path of Pienaar, who stabbed it past Fulop from close range with Phil Bardsley unable to intervene.
And Fellaini sealed the points when Pienaar found himself in space on the right as Calum Davenport inexplicably backed away from him, and he made the most of the opening to square for the Belgian, who fired past Fulop first-time to seal the victory.