The Manchester United midfielder caught out Maarten Stekelenburg as he scored from distance in the first half, with Didier Deschamps's side holding on to claim all three points.
Jordan Henderson had a hand in both goals as the Three Lions made it two wins from two in World Cup qualifying after seeing off the Group F minnows at Wembley Stadium.
The World Cup holders were far too strong on Saturday, and strolled to victory thanks to the Bayern star's efforts while Toni Kroos also found the net.
The Atletico Madrid striker bagged a brace as Didier Deschamps' charges registered their first victory in the 2018 World Cup qualifying phase at Stade de France on Friday.
The Real Madrid star returned to international weekend with style, opening the scoring after just 70 seconds before adding a further three later in the game.