Arsenal had taken the lead only four minutes earlier, through Mesut Ozil, but with a handsome advantage beckoning, on-loan Barcelona forward Deulofeu smashed home to earn his side the point that their endeavour deserved.
Having seen Chelsea, Manchester City and Manchester United drop points on Saturday, Arsenal are nonetheless five points clear of Liverpool and Chelsea ahead of their trip to City next weekend.
Defending champions United, meanwhile, are now 13 points behind Arsene Wenger's side in ninth place.
"We regret we were 1-0 up and couldn't keep a clean sheet," said Arsenal manager Wenger, whose side will look to dot the i's and cross the t's of Champions League qualification at Napoli on Wednesday.
"We were caught a bit on the flanks. This team has a fantastic attitude and response always. They give everything. We know we have quality and at least we took a point.
"There is always room for improvement. The three points would have been better, but the attitude and quality of the players is there and is a good basis for improvement."
It was another spirited performance from Roberto Martinez's Everton, who won 1-0 at United on Wednesday and continue to stalk the Champions League contenders, sitting a point below fourth-place City in fifth.
"Their goal came from nothing, but to display the character and come back to score with a goal of that quality was fitting for a game of that standard," said Martinez.
Everton were unchanged from the team that had prevailed at Old Trafford, while Arsenal recalled Kieran Gibbs, Mikel Arteta, Jack Wilshere and Olivier Giroud following Wednesday's 2-0 victory at home to Hull City.
Buoyed by their first win at United since 1992, Everton took the game to Arsenal from the off, with Kevin Mirallas drilling a low cross across the face of goal and Sylvain Distin hooking wide from the edge of the box.
Mirallas also shot wide after a break led by Ross Barkley, before Arsenal provided the first glimpse of their attacking capacity in the 27th minute.
A sweeping cross-field move culminated in Santi Cazorla playing a low ball into the box from the right that eluded the sliding Gibbs by inches.
With half-time nearing, and dissent in the crowd growing, Arsenal roused themselves, but when first Giroud and then Aaron Ramsey were sent through, Everton goalkeeper Tim Howard twice flew out to block with his legs.
The assault continued in the second half, with Howard obliged to save a header from Cazorla, but Everton served a reminder of their threat on the break when Steven Pienaar extended Arsenal goalkeeper Wojciech Szczesny with a 25-yard shot.
Back at the other end, Howard was called into action again to push away a volley from the sliding Ramsey, before the impressive Barkley stung Szczesny's palms with a rasping drive.
With 23 minutes to go, Wenger elected to twist rather than stick, introducing Theo Walcott, Tomas Rosicky and Mathieu Flamini in place of Wilshere, Ramsey and Cazorla.
Flamini thrashed a shot inches wide shortly after coming on, but Everton continued to menace, with Mirallas hitting the side netting and Distin heading over the bar.
The game had opened up, and with 10 minutes remaining, Arsenal went ahead.
Rosicky's deep cross was knocked back across goal by Walcott and although Giroud completely miscued his volley, Ozil was on hand to lift the ball into the roof of the net from close range.
It looked destined to be the winner, but with 84 minutes on the clock, Deulofeu collected the ball on the right-hand side of the box, shifted it away from Gibbs and thrashed a rising shot past a startled Szczesny.
Romelu Lukaku threatened twice in the closing stages, but Arsenal came closest to snatching all three points when Giroud rattled the crossbar with a 25-yard half-volley in added time.