LeMond won the 77-mile stage from Villard de Lans in a provisional time of 3 hours, 17 minutes, 53 seconds, edging Laurent Fignon into second place in the closing sprint.
But the American gained no time on Fignon in the last mountain stage of the tour and remained 50 seconds behind with virtually no hope left of preventing the Frenchman from winning in Paris on Sunday.
'Will Be Difficult'
"It will be difficult to make up 50 seconds now because the final time trial is so short," LeMond said.
With a flat 78-mile stage to l'Isle d'Abeau on Saturday, LeMond's remote chances rest on the 15-mile individual time trial from Versailles to Paris on Sunday.
"I'll be fighting right to the last kilometer," the 1986 winner promised. "You never know what can happen in this race."
Fignon, the 1983 and 1984 winner who took the yellow jersey from LeMond two days ago, said: "He deserved to win today. I had to fight during the stage but I felt very strong and I think I could have broken away if I'd tried.
"Every day victory is getting closer and I'm getting stronger and more confident."
Last year's winner, Pedro Delgado of Spain, came in third in the same time as LeMond and Fignon to stay third overall, 2 minutes and 28 seconds behind the Frenchman.
5 Tour Leaders
The three were in a group of five tour leaders who broke away on the Col de Porte, the first of the stage's three passes, in an attack led by Fignon.
The two others, Gert-Jan Theunisse of the Netherlands and Spaniard Marino Lejarreta, finished with the breakaway group 2 minutes and 10 seconds ahead of the main pack.
In the women's tour, Jeannie Longo of France captured her fifth consecutive stage victory today to continue moving away from the field.
Longo, the overall champion in 1988 and 1987, won by 1 minute, 35 seconds over American Inga Thompson.