Having won only three games all season, Christian Bracconi needed a miraculous end to the season to stand a chance of survival, but they were condemned to the second division by former defender Sebastien Squillaci.
Aboubacar Camara gave Ajaccio a fighting chance as they took a fourth-minute lead.
However, Florian Raspentino levelled just after the half hour and Squillaci sealed victory for Bastia with two minutes remaining to seal the visitors' fate.
Sebastien Corchia's third goal of the campaign was enough to record a 1-0 victory over Reims, and move Sochaux to within two points of safety.
Dimitar Berbatov's fifth goal in nine appearances gave Claudio Ranieri's side victory, the Bulgarian perfectly executing a lob over David Ospina, returning the club to Europe's top table for the first time since 2004-05.
Lille moved seven points clear in the third and final Champions League berth with a goalless draw against Marseille, a result that does nothing to help Jose Anigo's side and their late push for a Europa League place next season.
Bordeaux sent Coupe de France finalists Guingamp to a fifth straight league defeat with Cheick Diabate starring for Francis Gillot's men as they won 5-1.
The Mali striker took his season's tally to 11 with a first-half hat-trick that leaves Guingamp just two points above the drop zone, with Sochaux snapping at their heels.
