Toffees boss David Moyes chose to rest Leighton Baines, Nikica Jelavic and Tim Cahill, and the first half was a bore fest - but the game burst into life in the 52nd minute when Magaye Gueye smashed in the opener.
And Everton made sure of the points with a flurry of goals, which began in the 75th minute with a curler from Steven Pienaar. Leon Osman followed suit a minute later and substitute Victor Anichebe completed the rout with a deflected shot.
Moyes handed James McFadden his first start since the Scot returned to the club in October, while Denis Stracqualursi, Osman, Marouane Fellaini and John Heitinga also came into the side.
Sunderland, whose only change saw David Vaughan replace the injured Nicklas Bendtner, had extra motivation to beat the Toffees after losing out in an FA Cup quarter-final replay last month.
Everton are a real bogey club for the Black Cats, though, with their last victory in the Premier League coming back in December 2001.
The visitors could also point to a statistic in their favour, however, with Moyes looking for his first win over a team managed by Martin O'Neill at his 10th Premier League attempt.
The first half had the look of an end-of-season affair, with Everton's impending cup date also surely a factor, although it was the hosts who enjoyed the majority of the possession and chances, such as they were, in the first half.
Lee Cattermole was booked for bringing down Pienaar 22 yards out but McFadden's free-kick was eventually scrambled away, while in the 27th minute Gueye chose to pick out Pienaar rather than shoot and the midfielder skied his effort.
Osman then found Fellaini 10 yards out only for the midfielder to slice his shot well wide, while at the other end Sunderland's first real chance of the game was a spectacular one as Phil Bardsley crossed for Stephane Sessegnon, who guided his overhead kick just wide.
The game was gradually opening up and McFadden curled a shot that at last forced Simon Mignolet into a save, albeit a comfortable one.
Everton continued their probing at the start of the second half, forcing three corners in quick succession, and from the third in the 52nd minute they at last broke the deadlock.
McFadden's cross was cleared but only as far as Pienaar, who headed the ball into the path of Osman 15 yards out. His fierce shot was blocked by Mignolet but he could not hold on and Gueye smashed in his first Everton goal from a tight angle.
McFadden had been heavily involved in the game on the right and he beat Jack Colback with a surging run into the area but his attempted cutback was blocked by Mignolet.
Both managers made changes, with Kieran Richardson and Ji Dong-won coming on for Sunderland while McFadden was replaced by Royston Drenthe, making his first appearance for almost three weeks after returning from extended compassionate leave.
Sunderland really had not been in the game all afternoon and only a last-ditch tackle from Vaughan prevented Osman from getting his shot away, while Stracqualursi flicked an effort high over the bar.
And two near identical goals in as many minutes ensured the points were wrapped up in favour of the hosts.
First the ball was played along the edge of the Sunderland area to the impressive Pienaar, who showed his quality with a lovely curling shot into the far corner in the 75th minute.
And little over 60 seconds later Osman expertly took down a long ball on his chest before turning inside and placing another superb shot in almost the same spot.
Sunderland were all over the place and in the 81st minute they conceded again. Pienaar wriggled away from two defenders in the corner and picked out substitute Anichebe, who had only been on the field for four minutes.
His first attempt at a volley merely flicked the ball up in the air, but he caught his second well enough, although Mignolet was beaten only because of a huge deflection off Colback.