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.
Swim Week Miami Beach 2014 [PHOTOS]