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 Saint-Germain who drew 0-0 with Ajaccio at home on Friday to reach 39.
Girondins Bordeaux recorded their first league victory since mid-November when they won 2-0 at Stade Rennes to leapfrog the hosts into fourth place, tied on 32 points.
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 told the club's website.
"We are fully aware that this kind of showing would not be enough to win the next game," added Garde.
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 equal 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.
"This goal was the only thing missing for me to continue growing as a player. I am very happy," Umtiti told French channel Canal+.
"We showed our resources. We were not that good but we will only think about the three points we took," said the defender.
In Rennes, Yoan Gouffran scored his eighth league goal this season to put the visiting Bordeaux ahead in the 57th minute.
Henri Saivet powered home a splendid half-volley to double the lead nine minutes later as Bordeaux clinched their first win after five consecutive league draws.
Substitute Gaetan Charbonnier was twice on target in 12 minutes late on to earn champions Montpellier a deserved 2-0 victory over Lorient, who fell to sixth on 31 points as Montpellier climbed to ninth on 29.
Nolan Roux scored the fastest goal of the season after 21 seconds for 2011 champions Lille, who blew the lead twice to draw 2-2 at basement-side Nancy.
Nancy captain Andre Luiz left the pitch in tears in stoppage time after playing his last game in an eight-year spell before he heads back to his homela
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