The defeat ended Marseille's fleeting hopes of a finish in the places for next season's Champions League or Europa League.
Cornet opened his account midway through the first-half and the visitors spurned further chances to increase their advantage.
Marseille's quest to gain parity suffered a blow during the second-half.
Duje Caleta-Car was given a straight red for a foul on Lyon midfielder Martin Terrier as he closed in on goal.
Diminished, Marseille succumbed in the final stages of the match. Substitute Moussa Dembele made it 2-0 in the 84th minute and Cornet notched up his second two minutes later.
"I think we deserved the three points on the basis of the entire game," said Lyon coach Bruno Genesio. "It wasn't only our spirit - that's one of the basic things - but what we also did. We were solid and organised in defence and created some good chances."
Lyon, who have 66 points, will confirm third spot with victory at home to relegation threatened Caen on 18 May. "We're not in the Champions League yet," added Genesio. "One more win will get us there."
Lille effectively wrapped up second place on Sunday following a 1-0 win over Bordeaux. Loic Remy hit the winner in the first-half. Lille have 72 points from their 36 games and have a +14 goal difference over Lyon.
At the other end of Ligue 1, Guingamp dropped to the second division after a six year stay in the top flight.
They drew 1-1 with Rennes. Marcus Thuram missed a stoppage time penalty that could have given them victory and the chance to fight on another week
Dijon, Caen, Monaco and Amiens are fighting to avoid the second relegation place and the relegation play-off slot.