With Phil Scolari's side firing five past Middlesbrough earlier in the afternoon, the Gunners needed a victory to stay in touch at the top.
Their task was made that much harder as early as the ninth minute when Leon Osman exchanged passes with Steven Pienar on the left side of the Arsenal box, before sliding in to poke the ball past Manuel Almunia from five yards out.
Having failed to respond against Hull City in the last match at the Emirates, the pressure was on Arsene Wenger and his boys, especially as Everton have yet to be beaten on their travels this season.
Robin Van Persie raised the home side's hopes on 15 minutes when he took a long pass on his chest inside the area and quickly got his shot off, but Tim Howard was equal to the effort and spread himself well to block the shot from point-blank range.
Emmanuel Adebayor was getting into some good positions, but typically missed a batch of opportunities.
Osman was unlucky in the 19th minute when his drilled left-foot shot was deflected wide of the left post off the body of Mikael Silvestre.
Van Persie should have done better on 25 minutes when he was teed up by Emmanuel Eboue on the right but he fired his shot from the edge of the area high over the bar.
The Dutchman was on target a few minutes later when he curled in a free-kick from the right side of the area, but Howard punched the ball away to safety.
Gael Clichy prevented his side from going further behind in the 36th minute when he cleared off the line from Joleon Lescott's headed effort.
Cesc Fabregas raised home fans pulses in the 40thth minute with a shot across goal that had the Toffees keeper beaten but flew just wide of the left post. The young Spaniard did the same two minutes later to the frustration of the Gunners faithful.
Everton for the part were not only encouraged to be in the lead at half-time, but David Moyes players also had a better share of the possession than their hosts.
Having lost club captain William Gallas before the game, the Gunners suffered a further setback when his deputy Kolo Toure injured his shoulder and had to be replaced by Walcott at the beginning of the second half.
That was in itself a declaration of attacking intent and the dividends were collected within three minutes when Samir Nasri equalised with a low drive from a central position that went beyond Howard's outstretched arm to finish in the bottom left corner of the net.
The goal spurred the Gunners and their fans on and the tempo quickened to a pace more akin to Wenger's side's style. Van Persie should have given his side the lead on 55 minutes, but spooned a right-foot shot high over the bar from ten yards out.
Van Persie had a good claim for a penalty waived a way by referee Peter Walton.
The Gunners continued to press forward and were rewarded for their adventure in the 69th minute when Van Persie was on hand to nod the ball home from close range after Howard's save from Fabregas' shot rebounded up to the striker.
Walcott sealed the points in the final minute with a low drive from just inside the right side of the area, after fellow substitute Abou Diaby had cleverly pulled the ball back for the England star.