Arsenal thought they had the points wrapped up when Mesut Ozil tucked home the opener with 10 minutes remaining only for Deulofeu to equalise moments later with a thumping finish past Wojciech Szczesny.
It was a deserved point for Everton who dictated much of the first-half pace with Bryan Oviedo and Seamus Coleman looking particularly threatening down the flanks.
But Arsenal spurred into life five minutes before the break and fashioned a couple of good openings as Olivier Giroud and Aaron Ramsey produced smart stops from Tim Howard.
Both sides carved out opportunities in a pulsating second half before Ozil arrived at the back post to send the Emirates into delirium - only for Deulofeu to lash home and set up a nervy final five minutes.
Giroud struck the crossbar with a stunning volley in injury-time but the visitors held on for an important point while Arsenal extended their lead at the top to five.
44’ – SAVE: Giroud is in! This time the flag stays down and, after his shocker against Cardiff, the Frenchman plays on. Can he lift it over Howard? No! The keeper spreads himself and it bounces clear.
45’ – SAVE: Arsenal have sprung into life. Ramsey throws in a smart dummy, skips past his marker and receives the ball from Giroud. Howard produces another good stop to keep it scoreless.
67’ – CHANCE: Pienaar roams free down the left and delivers a clever pass back to Barkley who lashes an effort at goal which is beaten away by the Arsenal stopper.
80’ – GOAL: Arsenal 1-0 Everton: Walcott heads it back across goal, Giroud swings and misses but Ozil arrives to tuck home. Massive goal for the Gunners.
84’ – GOAL: Arsenal 1-1 Everton. It's swung in from the left. Lukaku does enough to help it into the path of the new boy, Deulofeu. He throws in a quick shimmy before lashing a shot past Szczesny. What a strike.
90+3’ – CROSSBAR: Giroud smashes a half-volley against the crossbar from the edge of the area. That is a tremendous hit!
Arsenal have 35 points from 15 Premier League matches this season. Only in 2007/08 (37 points) have they had a better PL record at this stage (finished third). (Infostarda)
Everton have lost one of their opening 15 top flight matches for only the fifth time, and the first since 1978/79. (Infostrada)
All nine of Mesut Ozil's league goals in 2013 (for Real Madrid and Arsenal) have been scored at home. (Infostrada)
Everton are winless in 13 Premier League matches against Arsenal (Infostrada)
Did Arsenal demonstrate the required bottle to win the league? When Ozil popped up in the 80th minute, many fans would have been forgiven for dreaming of the title. But Deulofeu struck late to ensure Arsenal had to settle for a point. On reflection though, Arsene Wenger should consider this one point gained rather than two dropped.
MAN OF THE MATCH
Laurent Koscielny (Arsenal): Managed the threat of Romelu Lukaku with real maturity and it is no fluke that the Belgian’s main sights of goal were from distance.
Arsenal: Szczesny 7, Jenkinson 6, Koscielny 8, Mertesacker 6, Gibbs 6, Arteta 6, Wilshere 6, Ramsey 6, Ozil 7, Cazorla 6, Giroud 6. Subs: Rosicky 6, Walcott 6, Flamini 6.
Everton: Howard 7, Coleman 7, Oviedo 7, Distin 6, Jagielka 7, Barry 7, Barkley 7, Pienaar 6, McCarthy 6, Mirallas 6, Lukaku 6. Subs: Deulofeu 7, Osman 6, Naismith N/A.
THE MATCH IN A TWEET