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 a 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.
The first-half was a cagey affair with good spells of possession for both sides, but there were few chances to show for it early on.
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 pose a threat, with Mirallas hitting the side netting and Distin heading over the bar.
The game had opened up, and with ten 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 past Gibbs and thrashed a rising shot past 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.
Fulham find a win
Earlier, relegation-threatened Fulham gave Rene Meulensteen his first win as their manager with a 2-0 victory over Aston Villa at Craven Cottage.
Steve Sidwell put the home side in front in the 21st minute when he scored against his old side after lofting the ball over the advancing Brad Guzan. Fulham, who previously hadn't scored two goals at home all season, then doubled their lead through a controversial penalty nine minutes later.
Alex Kacaniklic broke clear and charged into the box where he appeared to make the initial contact with Villa's Leandro Bacuna.
But the referee Mike Dean awarded a penalty and Dimitar Berbatov, after selling Guzan a dummy, rolled the ball into the bottom corner.
Victory saw Fulham, beaten 2-1 by Tottenham Hotspur in Meulensteen's first game in charge on Wednesday after he succeeded fellow Dutchman Martin Jol, climb one place into 18th spot but remain in the relegation zone.
However, their tally of 13 points left them level with London rivals Crystal Palace and West Ham United, the two clubs either side of them in the table, and in the bottom three on goal difference alone.