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Arsenal, unbeaten in 19 games in all competitions, moved above Spurs into fourth place in the league on goal difference, with both teams on 30 points.
The England International rubbed his head but appeared unharmed as he responded by gesturing the 2-0 lead.
Liverpool also fell behind but stormed back to beat Burnley 3-1 and cut the gap on leaders Manchester City to two points.
Liverpool are nine points clear of second-placed Tottenham Hotspur, who lost 3-1 at home to Wolverhampton Wanderers.
Everton had created most of the early chances as they looked for their first victory at Arsenal since January 1996.
The Gunners, looking to extend their unbeaten run to 14 games in all competitions, poured forward in search of an equaliser and the pressure paid off when Lacazette struck in the 82nd minute.
Arsenal and Chelsea were among seven teams to reach the Europa League knockout stage, while last year's runners-up Olympique de Marseille were eliminated at the group phase.
Bournemouth and Everton maintained their unbeaten starts to the season in a dramatic match in which both sides ended with 10 men.
Raheem Stirling and Bernardo Silva scored for the Premier League champions at Emirates Stadium.
Manchester United breezed to a 6-1 aggregate win over 10-man Bruges after a 5-0 return-leg rout of the Belgians at Old Trafford.
Results 121-130 of 190
