The result sees them stay second from bottom in the league table, five points from safety with just one more round of matches left this season.
Thomas Mangani tried his luck for the hosts in the sixth minute with a shot from distance, but failed to keep it on target.
Bastia were struggling to force themselves on Nancy, who went close again on 38 minutes through Mangani, before Lossemy Karaboue dragged his effort wide.
Then on the hour mark Sebastien Puygrenier restored parity for Nancy when he shot home from just yards out after collecting Mangani's corner.
However, Bastia regained their advantage in the 72nd minute when Modeste found the target with a long-range effort, consigning Nancy to Ligue 2 next season.