The Real Madrid defender nodded home the only goal of the game in the 83rd minute to give a much-changed Les Bleus the win.
France had the chances to make it a more comfortable evening at Marseille’s Stade Velodrome but failed to take them, substitute Karim Benzema even missing a penalty four minutes from time.
The hosts showed eight changes from their previous match, a 1-1 draw against Albania, while Zlatan Ibrahimovich was the headline absentee for Sweden having been rested following a goalscoring effort in Montenegro on Saturday.
France wasted no time getting going, Dmitri Payet trying his luck inside 20 seconds but failing to hit the target.
By the time 10 minutes had passed Sweden were struggling for a foothold, Josuha Guilavogui and Layvin Kurzawa also reeling off shots, while Bacary Sagna made early progress down the right.
Sweden took their time to make inroads at the other end, Sebastian Larsson hitting the wall when the recalled Eliaquim Mangala gave away a free-kick.
Varane produced a weak header when his first chance of the night arrived in the 26th minute, while Mathieu Valbuena’s overhead kick squirmed wide soon after.
Sweden continued to ride their luck, Antoine Griezmann twice letting them off, before Isaac Kiese Thelin offered a volleyed reminder just before half-time.
Andreas Isaksson ensured the stalemate continued with a pair of fine saves early in the second period, denying Andre-Pierre Gignac with feet then brilliantly blocking Griezmann’s close-range attempt.
With substitutes starting to disrupt the flow and Isaksson again on hand to prevent Moussa Sissoko in the 79th minute a goalless draw seemed a certainty.
Instead Varance, wearing the captain’s armband, finally found the net when he came up for a corner and buried his header in the bottom corner.
Three minutes later Benzema had the chance to double the home side’s lead but he was wasteful from the spot.