Arsenal broke through in the second half.
Emery praised summer signing Lucas Torreira for keeping his discipline after an early booking in what was his first Premier League start.
Ex-Arsenal man Theo Walcott won a unsafe free kick with a clever dribble into the box, and Gylfi Sigurdssson hoped his 30th minute effort would punish the Gunners.
Arsenal kept their first clean sheet of the season and had 36-year-old Cech to thank for keeping the visitors at bay in the first half.
However, Arsenal's patience was rewarded after half an hour, with Henrikh Mkhitaryan stealing possession deep in his own half and picking out Iwobi on the counter, who was able to cross for Aubameyang to tap in on his European debut for the club.
"It's really frustrating and I'll tell you why", said Silva, Everton's manager.
"I believe that if they do things in the right manner, Arsenal have everything required to be a massive club".
If that move show-cased the best of the attack-minded Bellerin, Everton's next chance underlined the Spaniard's defensive frailties.
Cristiano Ronaldo red card: Juventus star Emre Can apologises for ‘sexist’ comments
The red card was controversial, with Juve chief Massimo Allegri claiming VAR would have seen the decision overturned. But it looks like in a bid to stand by Cristiano Ronaldo , another summer recruit Emre Can, has crossed the line.
The Gabon worldwide also saluted Gunners goalkeeper Petr Cech's display, and stated his belief that his team were on the rise.
Richarlison, back after serving a three-match ban, was a constant menace to the ponderous Arsenal defence and he went close again with a low curling effort from the edge of the area.
Theo Walcott admits he "fell out of love with football" towards the end of his time at Arsenal as he struggled for regular game time under Arsene Wenger.
Unai Emery has warned his Arsenal side to be prepared for a tough encounter when they welcome Everton to The Emirates on Sunday afternoon.
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.
But the Merseysiders nearly found a foothold when Michael Keane's downward header was tipped away by Cech, and they then brought on Bernard and Cenk Tosun for Walcott, applauded by the home fans as he made his way off, and Calvert-Lewin.
The turning point came in the 56th minute when Lacazette picked up a short pass from Aaron Ramsey on the left channel, took a touch, and curled a shot in off the far post for his second goal of the season. The Turkey global is still looking for his first goal of the season.