Olivier Giroud fired world champions France to a 1-0 victory in Reykjavik as Iceland lost a home qualifier for the first time in six years.
On the fringes of things at Chelsea, Giroud remains an integral part of France's plans eight months out from Euro 2020, and his 37th goal for his country came from the penalty spot midway through the second half.
It came after Antoine Griezmann went over in the area, and amid Icelandic protests about the decision by Italian referee Gianluca Rocchi.
But France were the better team for long stretches of the game, worthy of becoming the first visitors to leave Iceland with three points since Slovenia earned a 4-2 win in World Cup qualifying in June 2013.
France beat Iceland 4-0 in Paris earlier in the group but their preparation this time was disrupted by losing N'Golo Kante to injury moments before kick-off, with Moussa Sissoko taking his midfield berth.
France were already without three star men in Kylian Mbappe, Paul Pogba and captain Hugo Lloris. Raphael Varane skippered the team and Steve Mandanda took over from Lloris in goal, as Les Bleus looked to avoid another away-day blip, having lost to Turkey in June.
They kept Hannes Halldorsson in Iceland's goal busy enough before the break, with Benjamin Pavard, Griezmann and Kingsley Coman threatening, but France hit their stride in the second half.
Halldorsson repelled a Griezmann free-kick, before France's Barcelona forward made a hash of a volley. Griezmann thumped another shot wide from 20 yards, searching for a goal that would have taken him to 30 for his country, putting him level in sixth place on the all-time list alongside Just Fontaine and Jean-Pierre Papin.
The penalty award came in the 64th minute when Griezmann went down theatrically after colliding with Ari Skulason.
With Griezmann receiving a little TLC off the pitch, it was Giroud rather than the Barcelona forward who took the spot-kick, firing home to found the bottom-right corner.
It was little surprise Griezmann was able to carry on, and he threatened shortly after with a raking shot that Halldorsson gathered.
Blaise Matuidi hit the post from 10 yards with a scuffed left-footed strike, before almost knocking out defender Victor Palsson with a thumping volley and Halldorsson saved with his legs from substitute Wissam Ben Yedder late on as France stayed unbeaten against Iceland, their record now showing 11 wins and four draws against Friday night's hosts.