The Manchester United midfielder has struggled to live up to his £89million price tag since returning to Old Trafford in the summer but he scored the winner for Les Bleus with an impressive 30-yard strike on the half-hour mark.
France, losing finalists on home soil at Euro 2016, are level on seven points with Sweden at the top of the group after the Scandinavians beat Bulgaria 3-0.
First-half goals from Ola Toivonen and Oscar Hiljemark sent the Swedes on their way before Victor Lindelof added a third after the break.
Elsewhere in Group A, 10-man Luxembourg claimed their first point as Aurelien Joachim's late free-kick secured a 1-1 draw away against Belarus.
The visitors had Dirk Carlson sent off in the 44th minute and looked set for their third straight defeat in the pool when Belarus substitute Pavel Savitskiy headed home with 10 minutes to go.
Christian Benteke scored after just seven seconds - the fastest goal in World Cup qualifying history - as Belgium beat minnows Gibraltar 6-0 to maintain their perfect start to Group H.
The Crystal Palace striker went on to score a hat-trick while Axel Witsel, Dries Mertens and captain Eden Hazard completed the rout for the leaders.
Greece also made it three wins out of three with a comfortable 2-0 victory in Estonia.
Vasileios Torosidis took just two minutes to put the visitors ahead before Konstantinos Stafylidis' free-kick sealed the points just after the hour mark.
In the group's other game, Roma striker Edin Dzeko scored both goals as Bosnia-Herzegovina won 2-0 at home to Cyprus.
Andre Silva hit a first-half hat-trick to help Euro 2016 winners Portugal to a comprehensive 6-0 victory over the Faroe Islands in Group B.
The Porto striker opened the scoring on 12 minutes, added his second midway through the half and then completed his treble eight minutes before the break.
Cristiano Ronaldo, Joao Moutinho and Joao Cancelo added goals in the second half to complete the demolition.
Switzerland remain top of Group B on nine points after they eventually beat a stubborn Andorra side 2-1 at Estadi Nacional.
The opener came from the penalty spot after Admir Mehmedi was brought down in the area and defender Fabian Schar slotted home.
The visitors finally got their second when Xherdan Shaqiri found Mehmedi to nod home with 13 minutes remaining as they looked to ease to victory.
Andorra caused some concern through Alexandre Martinez's 25-yard strike in stoppage time but Switzerland held on to maintain their 100 per cent start.
Meanwhile, Hungary beat Latvia 2-0 in Riga thanks to goals from Adam Gyurcso and Adam Szalai.
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