Stumbling Lyon miss chance to retake third in Ligue 1
Paulo Fonseca's men have gone four league games without a win to slip from the fringes of the title race to fourth, two points behind OM.
Just two weeks ago Lyon were set to move eight points clear of Marseille when leading their top-three rivals before a late collapse saw them slide to a 3-2 loss.
Le Havre were reduced to 10 men 10 minutes into the second half when Stephan Zagadou was sent off.
But Lyon mustered just one shot on target in a tame second-half display and are now only four points clear of fifth-placed Monaco and sixth-placed Rennes.
Gary O'Neil's Strasbourg fell six points off the European places after a goalless stalemate with Paris FC.
Toulouse ended a six-match winless run in the league as Mario Sauer scored a dramatic 99th-minute winner in a 4-3 victory at bottom club Metz.