Senior guard Jalen Jackson led the Southland Conference champions with 22 points and six rebounds, including 14 of 18 from the free-throw line.
Isaac Mushila added 15 points and 12 rebounds as Texas A&M-Corpus Christi (24-10) led for 38 minutes, but watched as Southeast Missouri State (19-17) rallied to tie the game with 3:07 left before the Islanders made key plays down the stretch won win.
The Redhawks were led by their dynamic backcourt of Chris Harris, who led the Ohio Valley champions with 23 points and Phillip Russell, adding 15 points and 10 assists.
Texas A&M-Corpus Christi moves on to face Alabama in the first round on Thursday.
Story of the game
Texas A&M-Corpus Christi came out hot, scoring the first six points of the game, capped off by a basket from Simeon Fryer, but Southeast Missouri State eventually tied the game at 13 thanks to a pair of three-pointers by Adam Larson.
The Redhawks took their first lead of the evening on a bank shot by Nate Johnson to go in front 18-17 with 9:54 to play in the first half, but Mushila keyed a 9-0 run by the Islanders by scoring five points during that stretch.
Larson nailed another triple to cut the lead to 28-25, but Texas A&M-Corpus Christi finished the half strong to take a 33-27 advantage into the locker room.
After baskets were exchanged early in the second half, Ross Williams buried one from long distance to put the Islanders in front 38-32 and the lead was increased to 43-34 after Mushila and Williams hit free throws.
Southeast Missouri State trimmed the deficit to 45-43 before the Southland champions went on an 8-0 run with layups by Jackson and Trevian Tennison.
With the score 61-52, the Redhawks made it a 62-61 game with 4:45 to play and free throws tied it at 64-64.
Jackson put Texas A&M-Corpus Christi back in front to stay with a trio of free throws and Tennyson made a huge shot in the paint to make it a 72-69 game until Russell's layup made it a one-point game again.
After more free throws, Russell had a chance to tie the game, but his three-pointer with three seconds was off the mark and Mushila sealed the win by hitting a free throw at the other end.