Lyon began the day in pole position and after Leonardo Jardim's Monaco put the pressure on with a 3-2 win over Guingamp, Bruno Genesio's men were forced to respond by beating GFC Ajaccio 2-1.
Teenage striker Cornet, who missed last week's win at Toulouse after a straight red card in the recent draw with Nice, fired Lyon into a two-goal lead before half-time after Rachid Ghezzal had given them an early lead direct from a corner.
Gregory Pujol reduced the deficit early in the second period and the visitors went close to snatching a point, but Bruno Genesio's side held on to move back into second place on goal difference above Monaco, who beat Guingamp 3-2 earlier on Saturday.
Monaco led 2-0 at half-time through Lacina Traore and Nabil Dirar, but needed Bernardo Silva's 76th-minute strike (see below) as Mevlut Erding and Brou Angoua scored for the away side.
Fourth-placed St Etienne were held to a goalless draw by Toulouse, but needed a penalty save by Stephane Ruffier from Wissam Ben Yedder to maintain parity and later had Loic Perrin sent off.
Nice, in fifth, also lost ground as they were beaten 1-0 at Nantes, Adrien Thomasson with the goal.