Caleb Berry then marched the Cardinals 73 yards in 12 plays to give Carranco his shot at the field goal.
Lamar (8-4, 5-3 Southland), led by Berry's 327 yards passing, held a 24-10 lead with 9:49 remaining in the third quarter. McNeese State charged back with Briscoe hitting David Bush on a 5-yard touchdown pass and then throwing to Celestie for the tie.
Berry, who also rushed for 91 yards, finished with 418 total yards and two passing touchdowns. Mark Roberts hauled in six passes for 103 yards and one touchdown.
Briscoe led the Cowboys (6-5, 4-4), throwing for 144 yards and two touchdowns.