Goals in each half from Egypt forward Kouka and Senegalese striker Issa Soumare helped Le Havre end their nine-game winless run across all competitions and climb off the bottom of the table until Sunday at least, when fellow strugglers Montpellier visit Strasbourg.
Lille substitute Chuba Akpom scored on his league debut in the seventh minute of stoppage time but it was too little, too late for the home team.
Lille have exceeded expectations in the Champions League, where they last week thrashed Feyenoord 6-1 to qualify directly for the knockout phase.
But on Tuesday, the team squandered a 2-0 lead against second-tier Dunkerque in the French Cup, before losing the penalty shootout.
Lille dropped to fifth in the French league on Saturday after their fourth defeat of the season.
Earlier Saturday, Nice capitalised on Monaco's defeat the night before to move third with a 2-0 win over 10-man Lens.
Ill-discipline cost the visitors dearly as Adrien Thomasson conceded an early penalty for a foul on Hicham Boudaoui. Gaëtan Laborde duly scored from the spot.
Lens defender Fucundo Medina was sent off with his second yellow card in the 57th and Jonathan Clauss sealed the win against his ex-club seven minutes later.
Monaco lost 4-1 at league leaders Paris Saint-Germain on Friday.
Rennes substitute Mahamadou Nagida scored late to seal a 2-0 win at Saint-Etienne in the late game, giving the team's new coach, Habib Beye, two wins from two games in charge.
Nagida, a 19-year-old defender from Cameroon, scored almost immediately after entering in the 84th minute for his second goal in as many appearances.
Arnaud Kalimuendo's early goal got Rennes off the mark at Saint-Etienne.
Beye is the ambitious Brittany club's third coach this season after Jorge Sampaoli and Julien Stephan.
Rennes spent more than 70 million euros in the winter transfer window. The win over Saint-Etienne lifted the team from 15th to 11th.
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