"(Ramsey scoring) puts in his mind he has to score as well," manager Arsene Wenger quipped.
The goals from midfield are helping Arsenal's pursuit of a first trophy since 2005, with the team also four points clear at the top of the Premier League.
In Europe, Arsenal can lose 2-0 in its final Group F game at Napoli next month and still advance. The Gunners have a three-point lead over Borussia Dortmund and Napoli after the German side won 3-1 in the other group game.
"We're not through yet we have to regroup again," Wilshere cautioned. "It's a tough group."
It didn't seem so tough from the start against Marseille, with the opener coming as some fans were still taking their seats.
Wilshere stormed down the right flank, cut into the penalty area past Lucas Mendes and lifted the ball into the net.
"In your minds you are on the back foot straight away," Marseille coach Elie Baup said through an interpreter. "Once you concede a goal like that you are in trouble."
It was Arsenal's quickest goal in the Champions League since Gilberto Silva netted after 20 seconds against PSV Eindhoven in 2002.
This was the free-flowing passing football Arsenal produce so well. What it struggled to produce, though, was another goal against a team already out of contention in the Champions League.
Another silky attack was completed by Wilshere squaring to Aaron Ramsey, but the midfielder managed to turn the ball straight to Steve Mandanda rather than placing it under the goalkeeper.
Arsenal was repeatedly sending the ball over the visiting defense to create openings, but the finishing wasn't as elegant.
When Ozil met Ramsey's dinked ball he couldn't get a clean shot away as it came off his shin.
Arsenal was gifted a chance to double the lead by referee Antonio Mateu Lahoz.
A penalty seemed to be harshly awarded when Ramsey was brought down by Nicolas N'Koulou just outside the penalty area, as replays showed. There was justice for Marseille, though, when Ozil's penalty lacked power and was easily saved by Mandanda.
"We had good control, maybe sometimes we were missing the cutting edge to finish off the game early," Wenger said.
The second half began just as frustratingly in front of goal, with Ozil's low shot turned round after Wilshere raised the ball to the Germany playmaker.
As frustrations grew, Olivier Giroud headed downwards and couldn't follow up with a shot before Mandanda collected the ball.
Any anxieties went when Arsenal's richly deserved second goal came.
Ramsey picked out Ozil on the right and a low cross was delivered to Wilshere, who dispatched the ball in the net with ease.
Arsenal goalkeeper Wojciech Szczesny then had his busiest spell as the game entered its final 20 minutes.
Substitute Florian Thauvin volleyed on the turn to Szczesny and it required Nacho Monreal to scoop ball clear from goal line.
Thauvin was denied again when Szczesny prevented the shot from going into the bottom right of the net.
Marseille left London still without a point and at the bottom of the group after five losses.
