The hosts started brightly, creating a number of chances in the opening 15 minutes, but it was Lyon who took the lead, Grenier slotting the ball in from inside the penalty area.
Gueida Fofana doubled the visitors' advantage in the second half, blasting a cross from Grenier into the top of the net.
Lyon's third came from the penalty spot after Julien Faubert brought down Fofana, Grenier converting the spot kick for his second of the game.
The visitors dominant spell continued, and two minutes later Alexandre Lacazette extended their lead to four with a strike from outside the box following a free kick.
The win moves Lyon back to second in the table, three points behind the leaders, while Bordeaux drop to ninth.