Lyon keeps Ligue 1 title hopes alive
Grenier fired a half-volley from long range into the top corner to lift the team one point ahead of Marseille, which hosts Brest on Saturday. Lyon still trails leader Paris Saint-Germain by eight points.
Lisandro Lopez gave Lyon the lead by heading into the bottom corner in the 29th minute, but Montpellier playmaker Younes Belhanda leveled in the 41st with a low drive from the edge of the box.
''It's a lucky victory, given Montpellier's good performance in the second half,'' Lyon coach Remi Garde said. ''We were in trouble but we gave nothing away. We need to show solidarity and that's what the players did today.''
Lopez was Lyon's most threatening player in the first half. He connected with a cross from Gueida Fofana in the eighth minute but his header lacked power to beat Montpellier goalkeeper Geoffrey Jourdren.
The Argentine striker also fired a long-range shot that Jourdren stopped in the 24th. But a few minutes later, Lopez scored his 10th league goal this season by heading in a cross from Grenier.
Montpellier wasted many clear-cut chances. Anthony Mounier capitalized on a defensive mistake from Fofana to be clean through on goal in the 10th, but Lyon goalkeeper Remy Vercoutre crouched to parry his side-footed effort.
Mounier again lacked the finishing touch in the 33rd. Unmarked inside the area, the Montpellier winger sent a cross from Remy Cabella over the bar.
It took a mazy run from the left wing by Belhanda to equalize before halftime. The Morocco international cut inside, faked a shot to create space and buried the ball into the bottom corner.
Montpellier got off to a better start in the second half and would have taken the lead with better finishing.
Cabella had a close-range volley blocked by Lyon leftback Mouhamadou Dabo in the 51st. Belhanda played Mounier in six minutes later, but the Montpellier winger chipped over the bar.
Vercoutre was then lucky to see an unmarked Abdelhamid El Kaoutari head the ball straight into his arms from close range in the 62nd.
Montpellier coach Rene Girard replaced a wasteful Mounier with Gaetan Charbonnier in the 70th to add more pressure up front and the substitute came close to finding the net, but headed wide in the 87th.
Vercoutre kept Lyon in the game in the 89th when he diverted a cross-shot from Cabella onto the post, and Grenier then pounced on a poor clearance by the Montpellier defense from a corner to score the winner from 25 yards.