He was offered an athletic scholarship to play Football by East Texas State University coach Ernest Hawkins.
Heading into his second year on the team, Cureton earned the starting job for the 1971 season, but only played 7 games due to injury.
The Lions went 8-2 during the regular season, losing only one NAIA game and defeating 3 ranked opponents and winning the 1972 LSC title with a 7-1 league record.
In the NAIA National Title game that was played in Commerce, Cureton scored a 1-yard touchdown in the 3rd quarter to give the Lions the lead.
Cureton's final year, he guided the Lions to a 7–4 record, finishing 3rd in the Lone Star Conference.
He had another stellar individual season, throwing for 905 yards and 3 touchdown passes despite missing a game due to injury.