Meeks would go on to claim the championship in the four-round event in Monroe, La., following a grueling seven-hole playoff against Australian Brandon Shong.
Jack Gnam, the defending champion from Ole Miss, finished eighth this week after climbing the leaderboard Saturday with a final-round 67 which was the lowest score of the day.
Charlie Miller, another senior for the Rebels, won the 2019 tournament.
On Saturday, Meeks and Shong were tied atop the leaderboard at 9-under-par following the four rounds of regulation play.
Meeks, from Walnut, Miss., started the closing round a shot back of leader Jack Hearn and carded a 72 score over the last 18 while the Irishman Hearn settled for a 74 and ended up dropping to third in the final standings.
Meeks was 1-over in the final round and 8-under for the tournament when he headed to the back nine on Saturday. He would make a bogey-5 to drop another shot and dip to 5-under with eight holes to play. Meeks managed to steady himself, though, and finished with six pars and two birdies to finish at even for the day.
He made birdies on the 14th and 15th holes before finishing with three pars to shoot 1-under on the closing nine.
Shong started the final day at 7-under and was three behind the leader when he teed off.
He had a chance to win the tournament in regulation when he made back-to-back birdies on the 15th and 16th holes to move to 5-under on the day and 12-under for the tournament.
However, he would find himself going to a playoff with Meeks to decide the winner after he made a double-bogey on the par-3 17th and then made a bogey at the last to drop three shots on the final two holes.
Shong was then forced to battle it out with Meeks in the playoff and saw the Mississippi golfer prevail at the end of a marathon day.
Meeks did not play for the Rebels this past season, sitting out his first campaign in Oxford as a redshirt. He went to Ole Miss as the No. 1 recruit in Mississippi and two-time state individual champion for Walnut High.
He came into the week playing well, tying for third in early July at the Magnolia Amateur in Hattiesburg, Miss. and at the Mississippi State Amateur in late June.
Shong is going into his senior year at New Mexico this fall. This past season, his best finish in a collegiate event was a tie for 17th at the N.I.T. hosted by Arizona in March.
Last past spring, Shong was medalist at one of the U.S. Open local qualifying events.
Shong was the only player who finished among the top five at the end to break par in Saturday’s final round. Hunter Bott from Montgomery, Texas, shot 73 and finished fourth at 7-under. Francois Jacobs from League City, Texas, also finished at 7-under as he posted a 74 in the final round.
The Cotton States tournament switched back to a four-round stroke-play event this year after deciding its winner the last 50 years through match play after using stroke play to set the match-play field.
The tournament has a long tradition of attracting top collegiate players and amateur golfers from across the world. Past competitors in the tournament include former PGA stars David Toms and Hal Sutton and current touring professional Marc Leishman.