The 19-year-old Umtiti, making his 22nd league appearance, scored the winner with 15 minutes remaining to put Lyon on 41 points from 20 games, ahead of Paris St Germain who drew 0-0 with Ajaccio at home on Friday to reach 39.
Third-placed Olympique Marseille could go level on points with Lyon if they win at 18th-placed Sochaux on Sunday.
Lyon, who were dumped out of the French Cup as holders last weekend by third-tier side Epinal, were made to work hard by their 19th-placed hosts despite opening the scoring in the 11th minute.
"We had a tough week. The players were willing to bounce back but they were feeling the pressure," coach Remi Garde said.
"We are fully aware that this kind of showing would not be enough to win the next game," added Garde, who did not mention the first place in his post-match comments.
Lyon started brightly as Maxime Gonalons, who was handed the captain's armband this week after striker Lisandro Lopez decided to give up the duty, headed home a Steed Malbranque corner to put his side in front after 11 minutes.
The home team went close to making it 1-1 in the 24th minute but Corentin Jean failed to slot the ball into an empty net from a neat Fabien Camus pass.
They were rewarded for their efforts when experienced playmaker Benjamin Nivet, 36, levelled the match with a superb volley in the 38th minute to match his best tally in a whole season with a seventh league goal this term.
Lyon bossed the game after the break but barely threatened the hosts' goalkeeper Yohann Thuram-Ulien until Umtiti took advantage of confusion in the Troyes defence following a corner to earn them the victory.
The Cameroon-born defender, starting for the ninth time this season, netted with his second attempt after his first shot on goal was cleared by a defender.
Fourth-placed Stade Rennes host Girondins Bordeaux later on Saturday, while Lorient, fifth in the standings, visit champions Montpellier who are 12th.