The loss prevented the Toffees from catching up with the five sides above them in the table, which leaves their European ambitions all but over for another year.
Paolo Di Canio's new charges appeared predictably invigorated by his leadership and played with sufficient bite and conviction to claim all three points.
The goal came moments before half-time as Leighton Baines surrendered possession to Stephane Sessegnon, who quickly bore down on goal and squeezed a shot past Tim Howard.
The Toffees were marginally better during the second period but never really fashioned out enough end product in the final third to seriously worry Simon Mignolet.
Here's a look at how the Everton players fared.
Tim Howard: 7/10
Howard reacted sharply early on to deny Danny Graham one-one-one and made a fine save to parry a Sebastian Larsson free-kick.
He was also competent enough dealing with crosses but will be disappointed at not being able to prevent Sessegnon's goal from trickling past him.
Seamus Coleman: 6/10
Matching up against his international colleague, James McClean, Coleman was never overly exerted at the back but won less than half of his challenges.
He was also especially uninvolved going forward, unable to produce an accurate cross or create a single chance for his side, which added to the Toffees' struggles in attack.
Leighton Baines: 5/10
This was arguably Baines' worst performance of the season. He was uncharacteristically sloppy to concede possession for the goal and found himself comprehensively beaten by Adam Johnson during one particular second-half exchange.
Considering he's featured in almost every minute of his side's season, it's possible this campaign's exertions are now catching up with him. He certainly didn't boost the arguments of those aghast at his exclusion from the PFA Player of the Year vote.
Sylvain Distin: 7/10
Distin was efficient enough at the back when coming up against Graham, but was let down by his fellow defenders around him.
The Frenchman displayed typical strength to deny his opposite man, was again unbeaten in the air and, unusually, ended the game as his side's top passer.
Johnny Heitinga: 6/10
Drafted in for the injured Jagielka, Heitinga struggled to replicate his new captain's influence, appearing especially tentative with his positioning.
He was bailed out by Howard in the opening minutes, when his hesitancy allowed Graham in, and was guilty of an overly clumsy challenge that again required his goalkeeper to rescue him from the resulting free-kick..
Darron Gibson: 5/10
Gibson was hauled off at half-time with an injury, although his input had been very minimal during the opening period.
The Irishman had a passing accuracy of a mere 56 percent—his lowest of the season by a considerable margin—and he only managed to make nine accurate passes in 45 minutes of football.
Marouane Fellaini: 7/10
Fellaini was one of the few Everton players to emerge with much credit from this game, having been his side's best performer playing in both defensive midfield and attack.
The Belgian won possession back for his side eight times, three more than any other player, created a couple of chances and was the Toffees' most active player in challenges, where he generally came out on top.
Steven Pienaar: 5/10
After a resurgent start to the year, Pienaar’s most recent decline will be a little worrisome for Everton, considering the generous amount they spent on the 30-year-old.
He was too often the culprit for a possession turnover, seemed predictable when trying to beat an opponent and was very rash with his passing, especially in the final third. The South African has obvious class and ability, but hasn't shown it enough this season.
Kevin Mirallas: 6/10
It was another frustrating match for Mirallas spent on the periphery of play. He produced a couple of glimpses of quality without ever threatening to take the game by the scruff of the neck, and was a little too lethargic in his defensive duties.
He still managed to create a couple of chances but Everton will have to spend the summer pondering ways of further involving their mercurial Belgian.
Leon Osman: 5/10
Osman started the match playing off Victor Anichebe and ended the game in a deeper berth but, in truth, he was ineffective in both positions.
He recycled possession ably enough, passing at 92 percent. However, he rarely influenced the game, created no chances and executed just 38 passes (his third lowest contribution of the season), despite his side absorbing a sizable 64 percent of possession.
Victor Anichebe: 5/10
Consecutive disappointing games for Anichebe, as the Nigerian failed to maintain possession or link up play with teammates to advance the Toffees up the pitch.
He never found enough time in the area to trouble Mignolet and only managed to unleash two wayward efforts at goal.
Nikica Jelavic: 5/10
The Croatian entered the fray at half-time but struggled to make a significant impact. He did manage to register three shots at goal but, once again, didn't benefit from his side's increasing preference to play a more direct brand of football.
Steven Naismith and Ross Barkley: n/a
Both players appeared with 15 minutes remaining but were unable to alter the result. Naismith struggled to make an impression, touching the ball just three times, while Barkley found little space to build on his promising contribution against Arsenal.