Kylian Mbappé joined France’s long list of injured attacking talents in the build-up, and the incoming Christopher Nkunku was unable to take an early opportunity as he fired straight at Elías Rafn Ólafsson from close range.
Didier Deschamps' men continued to create half-chances despite the hosts holding their own, with Jules Koundé’s deflected shot from range being held by Ólafsson.
Lucas Digne then had the Icelandic goalkeeper scrambling with an audacious free-kick, before Jean-Philippe Mateta scuffed his shot wide from Michael Olise’s cutback.
The hosts had a major scare when Ólafsson allowed Olise’s free-kick to slip through his hands, but the ball went wide, while Digne’s venomous attempt from the ensuing corner was blocked.
It was an Icelandic free-kick that resulted in the opener and inspired rapturous celebrations at Laugardalsvöllur in the 39th minute, as Victor Pálsson poked the ball over the line at the second attempt after Albert Guðmundsson’s initial delivery wasn’t dealt with.
While Iceland were dealt a blow with Sævar Atli Magnússon going off injured, they entered the break with their lead intact as Ólafsson saved Olise’s header and Mikael Egill Ellertsson got back onto the goalline to block Mateta’s follow-up.
Deliveries from Digne and Olise around the hour mark caused concern for Iceland, but Florian Thauvin’s acrobatic attempt fizzed off target and Nkunku also missed from a far bigger opportunity.
The AC Milan man made amends moments later, though, as he jinked inside Pálsson and curled his strike inside the far corner.
The visitors went ahead just five minutes later, when Maghnes Akliouche slid the ball to the back post for Mateta to mark his first international start with a goal.
Refusing to be downed, Iceland broke away for an immediate response that was sealed with a composed Kristian Hlynsson finish.
Mike Maignan slipped but recovered before Brynjólfur Willumsson could pounce, before Ólafsson held Khéphren Thuram’s tame shot as France lost their perfect record in WCQ.
However, they still sit top of Group D by three points despite Ukraine beating Azerbaijan. They also left Iceland with one point from their last three matches, although Arnar Gunnlaugsson will hope that it could make the difference as his side are within three points of second place.
Flashscore Man of the Match: Albert Guðmundsson (Iceland)