Sutton's go-ahead score came at the end of a 17-play, 79-yard drive, which included two fourth-down conversions. Lamar turned it over on downs on its final possession.
D'Shaie Landor threw for 283 yards and one touchdown, and ran for two scores for Southeastern Louisiana (3-1, 2-0 Southland).
Southeastern Louisiana had a 13-0 lead but Lamar scored 17 unanswered points.
Rodney Randle returned a kickoff 87 yards to give Lamar a 24-16 lead. But Xavier Roberson returned the ensuing kickoff 59 yards and Landor capped the short drive with a 5-yard touchdown run to pull to 24-23 at the end of the third quarter.