Everton looked the more likely to score the game's opener, but the hosts snatched a lead slightly against the run of play and built on their advantage to climb into sixth place in the standings.
The Toffees are now without a win in 25 visits to this part of North London in all competitions, but they certainly took no notice of the negative pre-match statistics as they edged the first half.
Richarlison fired in two shots on target, both of which Cech managed to deal with in a fairly routine manner.
The Brazilian winger, back in the side after a three-match ban, then dragged a shot wide when given some space inside the box, while Lucas Digne's free kick was pushed over the bar by an overworked Cech.
Former Arsenal man Theo Walcott was also guilty of squandering a good chance for the visitors, failing to get enough on his attempted chip over Cech when racing in behind, and Everton were so nearly punished in the closing stages of the first half.
An attempted cross from Aubameyang proved awkward for Pickford to deal with, and the England international was grateful to his crossbar for keeping it out.
Arsenal, who lost Sokratis Papastathopoulos to injury in the first half, required just 15 minutes of the second period to pull away from their opponents.
After coming close through an Aaron Ramsey drive and having a penalty appeal for Digne's handball rejected, Lacazette curled the ball into the top corner from 15 yards, which Aubameyang added to less than three minutes later.
The Gunners worked a three-on-one situation and, after a slip from Ramsey looked to have killed off the promising move, the Welshman managed to flick the ball through for Aubameyang to tuck home.
Replays showed that the Gabonese striker was a good yard offside, however, with that second goal taking all the wind out of Everton's sails.
Cech's eight saves ensured that Arsenal kept a first clean sheet of the season at the seventh time of asking, while at the same time making it back-to-back defeats for Marco Silva's visitors.
ARSENAL (4-2-3-1): Cech; Bellerin, Mustafi, Sokratis (Holding 39'), Monreal; Torreira, Xhaka; Ramsey (Welbeck 80'), Ozil, Aubameyang (Iwobi 69'); Lacazette
EVERTON (4-2-3-1): Pickford; Kenny, Zouma, Keane, Digne; Gueye, Davies; Walcott (Bernard 72'), Sigurdsson, Richarlison; Calvert-Lewin (Tosun 72')