Wilshere rewarded Arsenal's dominance with a second goal in the 65th minute, after Mesut Ozil had seen a penalty saved, to leave Arsene Wenger's side three points clear of Borussia Dortmund and Napoli at the top of Group F.
Arsenal can now secure their progress to the knockout rounds for the 11th successive season by avoiding defeat in their final group game at Napoli on December 11.
However, Napoli's loss to Dortmund in Tuesday's other group game means that should Arsenal lose in Naples, and Dortmund win in Marseille, qualification would be decided by goal difference in the three games between Arsenal, Dortmund and Napoli.
Arsenal manager Wenger made three changes to the team that beat Southampton 2-0 on Saturday, with Nacho Monreal, Tomas Rosicky and former Marseille midfielder Mathieu Flamini coming into the team.
With Marseille already eliminated, coach Elie Baup fielded a weakened team. Mathieu Valbuena was among five first-team players on the bench, and it did not take long for the visitors to fall behind.
Bacary Sagna freed Wilshere on the Arsenal right and the England midfielder lazily stepped inside Lucas Mendes's challenge before steadying himself and curling a left-foot shot into the top-left corner.
It would have been 2-0 six minutes later, after Olivier Giroud set Wilshere free again and he squared for Aaron Ramsey, but from 10 yards the in-form Welshman saw his shot cannon back off Steve Mandanda's chest.
Marseille's response was timid, Andre-Pierre Gignac heading over and then over-running the ball inside the Arsenal box, but the hosts failed to exploit an invitation to extend their lead shortly before half-time.
Ramsey appeared fortunate to win a penalty after tangling with Nicolas N'Koulou, the challenge occurring just outside the 18-yard box, but Ozil saw his spot-kick pushed away by Mandanda.
Arsenal continued to press early in the second period, but Giroud saw a shot deflected inches wide by Kassim Abdallah and when Wilshere released Ozil with an inventive chip, Mandanda flew out to save.
The entrances of Valbuena and Florian Thauvin as substitutes threatened to make it an uncomfortable closing half hour for Wenger's men, but in the 65th minute they scored the second goal that their persistence merited.
Ramsey was the instigator, sliding a subtle pass down the inside-right channel for Ozil, and the German partly atoned for his failed penalty attempt by centring for Wilshere to side-foot home his second goal.
Thauvin gave the Premier League leaders a couple of scares as the game approached its closing stages, but goalkeeper Wojciech Szczesny showed his alertness by saving sharply on each occasion.
Substitutes Santi Cazorla and Theo Walcott both spurned chances to seal matters for Arsenal in the dying stages, the Spaniard blazing over and the fit-again England winger toeing wide, but Marseille were already beaten.