With five hours remaining, 50 of the 61 cars were still running with the number seven Toyota of Britain's Mike Conway, Japan's Kamui Kobayashi and Argentina's Jose Maria Lopez out in front.
The number eight car, shared by world endurance championship leaders double Formula One world champion Fernando Alonso, Japan's Kazuki Nakajima and Switzerland's Sebastien Buemi, was a lap down.
Alonso's former McLaren Formula One team mate Stoffel Vandoorne, a Le Mans rookie, was also heading for the podium in the third-placed number 11 SMP Racing BR Engineering car shared with Russians Vitaly Petrov and Mikhail Aleshin.
That non-hybrid car was some six laps off the pace as the morning brought sunshine and blue skies after some light overnight rain.
The two Toyota TS050 hybrids had started first and second after dominating qualifying for the 87th edition of the endurance classic and led smoothly through the night at the Circuit de la Sarthe.
The racing was punctuated by crashes, with Venezuelan former F1 driver Pastor Maldonado hitting the barriers at Tertre Rouge in the number 31 Dragonspeed LMP2 after daybreak and bringing out the safety car.
Before that, the number 17 SMP that had been in third place spun out in the early hours at the Karting corner with Russian Egor Orudzhev at the wheel and the car proving too damaged to continue.
Toyota are the only major manufacturer in the top LMP1 category and the championship battle, in a super season that includes two editions of Le Mans, is a private one between their drivers.
Whatever happens, Sunday is guaranteed to see a Japanese driver win a major FIA-sanctioned world championship for the first time.
Alonso, who won Le Mans last year when he was also in his final Formula One season, is departing the world endurance championship after Le Mans.
The Japanese car giant has already clinched the manufacturers' championship and is sure to take the double with the number eight car out of reach of all but car seven in the standings.
(Reporting by Alan Baldwin, editing by Sudipto Ganguly)
