France dominated for the majority of the contest at the Stade Velodrome, but were unable to find a way past goalkeeper Andreas Isaksson until Real Madrid defender Varane powered home Antoine Griezmann's corner at the near post after 84 minutes.
There was still time for substitute Karim Benzema to blaze a penalty over, but Varane's club team-mate would not rue his miss as Didier Deschamps' team added to friendly wins over Spain, Portugal and Armenia this season.
Sweden's attack was largely toothless in the absence of star man Zlatan Ibrahimovic, with Malmo youngster Isaac Thelin passing up rare chances either side of half-time.
France coach Deschamps has used his team's lack of competitive action to experiment with different combinations so far this season and Tuesday's game was no exception as he made eight changes to the XI that drew 1-1 with Albania.
Marseille forward Dimitri Payet was one of the additions to the starting line-up and he cut in from the left and past a pair of challenges to curl a first-minute effort over the far post.
Sweden centre-back Andreas Granqvist made a telling interception to deny Josuha Guilavogui on the end of Griezmann's perfectly weighted pass before full debutant Layvin Kurzawa smashed a volley over when Paul Pogba scooped over the visiting defence.
Mathieu Valbuena took his turn to try the spectacular as he controlled Payet's chipped pass on his chest and sent an overhead kick off target.
Andre-Pierre Gignac unpicked the Sweden defence in the 36th minute, but Griezmann's touch deserted him and Isaksson was out to avert the danger.
Opposite number Steve Mandanda belatedly enjoyed his first action in the France goal five minutes before the break, getting down well to the bottom corner to keep out Thelin's hooked volley on the turn.
Isaksson was the goalkeeper back in the spotlight four minute after the interval with a superb point-blank save to stop Gignac from opening the scoring.
Thelin was allowed too much room to head over and France responded as Gignac came agonisingly close to turning home Griezmann's acrobatic effort before the latter blasted at Isaksson from close range on the angle.
The customary drip-feed of second-half substitutions served to dull the game's competitive edge before an unexpectedly dramatic finale.
Isaksson excelled again in denying sub Moussa Sissoko, but he had no chance when Varane finally broke the deadlock.
Oscar Wendt's handball threatened to give France a 2-0 lead, but Benzema joined the Sweden substitution in feeling sheepish with a woeful attempt from 12 yards.
