The 30-year-old bagged a brace to help the Gunners to a 3-2 win over the Toffees after they went behind to a Dominic Calvert-Lewin opener and Richarlison's goal on first-half stoppage time pegged them back.
Aubameyang now has 17 goals in the Premier League this season, moving him level with Leicester City striker Jamie Vardy in the race for the Golden Boot.
But the Gabon international, playing on the left wing with Eddie Nketiah up front, set the captain's example by putting in a tireless shift, tracking back to help out young Bukayo Saka in his defensive duties.
His work did not go unnoticed, with Arteta admitting he was proven wrong after initially doubting Aubameyang's work rate when he arrived at the club.
"It was an incredible amount of work Aubameyang was doing," he told Sky Sports.
"Before I took over I had my questions about him but he showed his commitment. I wanted him to show if he wanted to do it and do it [defensive work] physically."
Arsenal face a tough decision over whether to sell Aubameyang should the striker turn down a new contract, with less than 18 months to go on his current deal and Barcelona holding an interest.
But Arteta says he hopes the club can convince him to stay in north London, adding: "Aubameyang is our most important player.
"[There is] no doubt the impact he has in this team. We will have to convince him to stay with us."
Arsenal move up to ninth in the standings and are now just four points behind fifth-placed Manchester United as they race for a potential Champions League qualification spot heats up.