An unusually busy transfer window for Wenger also saw Olivier Giroud join Chelsea, while Theo Walcott could quickly come back to haunt the side he played with for over a decade when he returns to the Emirates in an Everton shirt.
Ramsey, Aubameyang, Mesut Ozil and Mkhitaryan all looked sharp and Wenger savoured the all-round display of his new-look attack.
Everton did improve in the second half and managed to pull a goal back through substitute Dominic Calvert-Lewin (64), but the hosts had the final say as Ramsey completed his hat-trick in the 74th minute, with Henrikh Mkhitaryan providing his third assist of the game.
However, Arsenal lost goalkeeper Petr Cech to a calf injury in a collision with Oumar Niasse as the striker hit the post in the second half.
By no means did Koscielny steal the goal from Aubameyang but the new man certainly would have scored if not for the French defender beating him to the ball.
The 28-year-old reunited with former Borussia Dortmund teammate Henrikh Mkhitaryan, who recorded three assists, and it was obvious that the pair had played together before. They should have bought at least one out and out winger to replace Sanchez.More news: Wynn Resorts (WYNN) Earns Neutral Rating from Nomura
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"Swansea was not the level we have played at recently and we have had to look at ourselves". A Wenger sort of player, definitely not Mourinho's cup of tea. He remains far off the pace he set last season, when he scored 24 times for the Gunners, while adding 10 assists, in 38 league appearances.
Allardyce switched to a back four for the second half and it nearly paid dividends as Walcott's low cross was turned onto the post by Oumar Niasse. How anyone can knock his career is beyond belief.
"The players are showing so much inconsistency that I face an uphill battle trying to get them to play at their best week in, week out". But the Gabon striker has submitted a medical certificate clearing him.
Arsenal fans chanted his name as he went off, a mark of respect for a great servant and top bloke.
Sam Allardyce has collected just three points from a possible 39 in away Premier League games at Arsenal (P13 W0 D3 L10), losing each of the last eight in a row, all at the Emirates. After a clever through-ball from Mkhitaryan, Aubameyang lifted the ball over Pickford to make it 4-0 and effectively end the match as a contest. If you think that Arsenal didn't play their best then think how the Everton players and fans are feeling this morning!