Stover's first collegiate field goal was set up when Sean Thomas intercepted Tulane's Devin Powell at the Green Wave 13-yard line.
Tulane had one last chance to tie the score but Cairo Santos missed a 48-yarder with 9 seconds left.
Elijah McGuire ran for 45 yard with a TD and caught seven passes for 94 yards for the Ragin' Cajuns (9-4).
Terrance Broadway 12-of-19 through the air en route to 143 yards with a pair of interceptions.
Powell completed 10-of-21 throws for 223 yards in relief of Nick Montana for Tulane (7-6), which fell in its final home game at the Superdome.
Next year the Green Wave will begin play at the new Yulman Stadium in New Orleans.