Kluivert, son of former Netherlands forward Patrick Kluivert, made his contributions before going off injured after 35 minutes
The match at the Allianz Riviera was played behind closed doors after a pitch invasion during last Sunday's game with Marseille.
Another Algerian international Hicham Boudaoui broke down the right before crossing for Kluivert, who side-footed home. Kluivert turned provider just after the half hour. He led a counter-attack, charging towards the Bordeaux box before feeding Amine Gouiri to finish easily.
Following his early heroics, Kluivert's game was over after a little over half an hour due to a thigh injury and replaced by debutant Calvin Stengs, who joined from AZ Alkmaar in July. French under-21 international Gouiri then took his tally for the season to three, by converting a penalty four minutes before the break.