Wes Brown's own goal took Everton into the Champions League places as Sunderland's relegation fears took a turn for the worse.
The former Manchester United defender unwittingly turned Gerard Deulofeu's cross past goalkeeper Vito Mannone to claim his side's sixth Barclays Premier League own goal of the season.
It was tough on Sunderland, who gave as good as they got for long periods before slipping to a fifth successive league defeat and with just six games left in which to pull off an escape of increasingly epic proportions.
But Everton, who had earlier seen Steven Naismith pass up two glorious opportunities to fire his side ahead at the Stadium of Light, got there in the end to leapfrog Arsenal into the top four.
The pre-match tribute to the Hillsborough victims was marred slightly as some spectators reacted angrily to others arriving late and not realising the period of silence had started.
However, once the formalities were completed, a relatively even first half got under way with the combatants embarking upon the contest with widely differing aspirations.
Everton arrived knowing a point would take them into fourth place with the Gunners in FA Cup action this weekend, while Sunderland knew anything other than a win would hammer another nail into their coffin.
In the event, both sides headed for the dressing room content with aspects of their first-half performance, but knowing much more was required to secure the reward they craved.
Black Cats boss Gus Poyet, who had holding midfielder Liam Bridcutt absent after his partner went into labour, opted to return to his tried and trusted 4-1-4-1 formation, this time with youngster Connor Wickham at its peak, and his side looked more compact as a result.
However, Everton's ball retention and fluid passing and movement ensured they were repeatedly stretched, with Leighton Baines and Deulofeu in particular causing problems in wide positions.
Romelu Lukaku and Fabio Borini missed the target at either end in a lively opening, but the visitors should really have been ahead with 14 minutes played.
Naismith spun superbly on to Baines' cross to leave Brown for dead, but from just 12 yards out blazed his right-foot shot high over the crossbar.
That was to become a theme of Everton's first-half play, with Lukaku, Deulofeu and Baines all uncharacteristically wasteful in promising positions.
Their profligacy might have been punished too had defender John Stones not rescued Baines 14 minutes before the break.
The full-back left his back-pass to keeper Tim Howard woefully short and Borini nipped in round him, only to see Stones block his shot from a tight angle at the near-post.
Deulofeu caused panic in the home defence with a determined run and inviting 51st-minute cross, but Mannone got down well to claim the ball before it could do any real damage, and Naismith stabbed a weak shot at the Italian after Seamus Coleman had recycled Deulofeu's repelled cross five minutes later.
However, Howard was relieved to see Borini's effort deflected wide as Sunderland established a bridgehead from which Phil Bardsley had a header cleared by Baines and Wickham a shot blocked in the resulting goalmouth melee.
But they might have gone ahead with 59 minutes gone when Ki Sung-yueng climbed above Naismith at the far post to meet Johnson's cross, only to head wide of the upright.
The Black Cats were almost punished twice within seconds when Deulofeu ghosted past Marcos Alonso on the right to send the ball across the face of goal, and Naismith failed to make the most of a mix-up between Mannone and Cattermole when he lifted the ball wide of the target, admittedly from distance.
Substitute Ross Barkley forced a save from Mannone after stabbing Sylvain Distin's cross towards goal with the visitors building momentum, although Alonso tested Howard from distance with the game opening up.
Howard was almost embarrassed by another long-range strike by Ki, but it was his opposite number whose success ran out with 15 minutes remaining.
Deulofeu once again skipped past Alonso and this time saw his cross cannon off the unfortunate Brown and into the net.
The Black Cats showed genuine signs of getting themselves back into the game as time ran by with Ki twice and Wickham going close, but there was to be no lifeline.