Lyon moved within two points of the top four after their 2-0 victory over Nice last weekend, and Les Gones came into this game looking to make it five wins on the bounce in all competitions.
Paulo Fonseca’s side started the game well and were in full control, but it took them 22 minutes until they got the breakthrough, when they were awarded a penalty after Nicolas Tagliafico was brought down by Etienne Youte Kinkoue.
Alexandre Lacazette stepped up and dispatched the ball expertly into the bottom-right corner.
However, the hosts went on to give Le Havre a penalty of their own less than 10 minutes later, as Ernest Nuameh brought down Yassine Kechta in the box.
The spot kick was then taken by Abdoulaye Toure, who rifled his shot into the roof of the net.
Nuameh thought he’d made up for his mistake just five minutes later though, as he thought he’d restored his side's lead, but his goal was ruled out for offside.
But it was Le Havre who went in ahead at the break as they took the lead in added time through Josue Casimir, after the forward kept his cool to slot a left-footed effort into the bottom-right corner of the goal.
The opening stages of the second half saw little in the way of goalmouth action, but Lyon went remarkably close to bringing themselves level with 57 minutes on the clock, but Tagliafico was denied by the foot of the right-post.
Lyon were in complete control of the game in the second half, however, Le Havre’s defence stood strong, limiting Les Gones' attack to very few clear-cut chances.
That resolve was eventually broken though, as Lyon brought themselves level with 12 minutes remaining, when Malick Fofana raced onto Georges Mikautadze’s pass before rifling a shot past Mathieu Gorgelin and just inside the near left-post.
The turnaround was complete just five minutes later when Mikautadze got himself on the scoresheet.
The goal came after the Georgian forward received the ball from a corner before firing a right-footed shot towards the near top-right corner.
The game was well and truly over in the seventh minute of added time, as Thiago Almada added a fourth by slotting into the bottom-right corner.
The home side saw the game out to secure all three points, to ensure they kept within two points of Ligue 1’s top four.
Meanwhile, Le Havre remain in danger at the foot of the table, still sitting in the relegation playoff position, just one point clear of 17th placed Saint-Etienne.
Flashscore Man of the Match: Georges Mikautadze (Lyon)