For the Gunners' youdominance was greater than the 5-2 scoreline suggests. From start to finish they outclassed a Toffees side dismally short of confidence and belief.
Oumar Niasse scored a late consolation for Everton but few Everton fans were left inside Goodison to see it.
The defeat may prove to be Koeman's last as Everton manager. Having invested heavily in the summer the Toffees should be far better than this. They are currently in the relegation zone and don't look like pulling away any time soon.
Koeman has failed to implement a tactical structure that brings the best out of his players. And that is where we begin our tactical analysis of Everton's defeat against a rampant Gunners.
Switch To Back Three Didn't Pay Off
With the pressure mounting and speculation increasing over his future at Goodison Koeman started the match with a back three, which became a back five for most of the opening period.
In theory it should've made Everton difficult to break down but in reality the Gunners carved their way through time and time again. In the opening 15 minutes Jordan Pickford had to make five important stops. By half time Wenger's side had registered 17 shots on goal, nine of which had been on target.
Only one of them found the back of the net but clearly Everton's defesive trio of Michael Keane, Ashley Williams and Phil Jagielka weren't able to keep Arsenal at bay. That was because the quartet in front of the back three contained Gylfi Sigurdsson, Nikola Vlašić and Rooney, none of whom are defensively minded players.
It meant runners from deep were often not properly tracked and that put extra strain on a fragile defence. Tom Davies was introduced at half time in place of Williams and Everton reverted to a back four with Keane and Jagielka at the heart of it.
It made little difference, however. Arsenal continued where they left off in the opening period and Everton couldn't deal with the movement of the Gunners' attackers.
Once Özil put Arsenal in front, there was only one winner and the ease at which Lacazette, Ramsey and finally Sanchez added to the scoreline was damning on slow, sluggish and timid Everton backline.
Calvert-Lewin Must Continue To Lead Everton Attack
One of the biggest issues Everton have had this season is the lack of pace in their side. Koeman has often filled his starting XI with creative No.10s, such as Rooney, Sigurdsson or Davy Klaassan, and it has meant the Toffees have been extremely one-dimensional.
It has also allowed opposition sides to move their defensive block upfield safe in the knowledge that Rooney, who has often led the Everton attack, lacks the pace to run in behind defences and would rather have the ball to feet.
One on the few players in the Everton squad who has the pace to stretch defences is Calvert-Lewin and he was finally deployed by Koeman as the Toffees' lone striker against Arsenal.
It wasn't an easy afternoon for the England Under-20 international. With Everton dropping very deep he was often the only Toffees player in the Arsenal half. But he was a willing runner and showed on more than one occasion he could bring a clearance down, hold up possession and wait for his team-mates to support.
He also provided a physical Everton have lacked, winning nine aerial duels despite being up against the lanky Per Mertesacker.
Going forward Calvert-Lewin has to be the man to spearhead Everton's attack. He will only get better with experience and currently offers something no other Toffees attacker can.
Arsenal fans have been waiting since the summer for Wenger to pull the trigger and put Sánchez, Lacazette and Özil in the same starting XI. At Goodison Park, the Frenchman finally did and it more than paid off.
It may sound a simple concept but good players enjoy playing alongside good players. So it's little surprise that the trio were quickly in sync against a shaky Toffees backline.
Their movement and constant rotation saw Everton players regularly pulled out of position or, if they choose to stand their ground, one of the three would have space to receive the ball and pick a pass.
In the opening period there were several neat passing moves involving Özil, Sánchez and Lacazette which usually ended with Pickford being forced into action.
However, in the second period, the three players combined to devastating effect. Lacazette led a counter and found Sanchez out wide. The French striker continued his run and that dragged Jonjoe Kenny out of position. Sánchez had room to cross and he perfectly found Özil who headed home.
All three were again involved in Arsenal's third, which was finished by Lacazette after being teed up by Özil.
The game was a snapshot of what Arsenal's attack could be going forward, however, with the German and Sanchez's future very much up in the air, it may be a short-lived concept.