Les Girondins keeper was called into action again on 38 minutes when he kept out Pujol's strike from the edge of the area as the visitors tried to stay on terms.
However, GFC finally broke through on the stroke of half time as Larbi steered his right-footed effort into the corner.
Within minutes of the restart, Bordeaux almost level when Wahbi Khazri fired wide before the Tunisian international missed the target again soon after.
Ajaccio then suffered a setback when Roderic Filippi was sent off with just under half an hour left.
However, Gazelec managed to double their lead as Larbi netted his second of the evening, following Jacques Zoua's cross.
Henri Saivet almost pulled a goal back for Les Girondins, but his shot drifted wide as GFC held on for their third win of the season.