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David Moyes' side already have an FA Cup final clash against Chelsea to look forward to later this month and are almost certain to have European football on their agenda again next season following this convincing victory.
South African midfielder Steven Pienaar opened the scoring early in the second half and record-signing Marouane Fellaini's late strike ensured Everton leapfrogged Aston Villa.
Although Villa can regain fifth place with a win over relegation-threatened Hull on Monday, Moyes' men are now just one point away from wrapping up a spot in the Europa League.
Ricky Sbragia's Sunderland face a nervous end to the season after a defeat which leaves them just four points clear of the bottom three with three games to play.
Sunderland suffered an early blow when Steed Malbranque was forced off for nine minutes after a clash of heads with Australian star Tim Cahill that left the Frenchman needing stitches.
When Malbranque eventually returned, Sunderland were clinging on as Cahill's header was punched away by keeper Marton Fulop.
Australia midfielder Cahill threatened again with a long-range strike in the 12th minute.
Everton were well on top and Jo and Pienaar combined well on the edge of the penalty area before the Brazilian fired just past the far post.
Sbragia's team went close with 27 minutes gone when Grant Leadbitter took aim from 20 yards, but his low drive sped past the post.
Anton Ferdinand had to get in a good block to deny Pienaar and full-back Phil Bardsley had to do the same to keep out Jo's effort seconds later after the home side had failed to clear their lines.
Leighton Baines almost caught Fulop out as his mishit free-kick sailed just over the bar before half-time.
Everton continued to dominate after the break and took the lead in the 48th minute when Jo held off Ferdinand before sliding the ball through to Pienaar, who poked his shot past Fulop.
The Black Cats might have been back on level terms within two minutes when defender Danny Collins met Leadbitter's corner with a firm header, but he directed the ball straight at Tim Howard.
Kieran Richardson forced Howard into a save with a curling free-kick but Sunderland never looked secure at the back and Fellaini sealed the points for Everton in the 71st minute.
Calum Davenport backed away from Pienaar after he had been found in space on the right and he squared for Fellaini to shoot past Fulop.
