Thomas shot 7-of-12 from the field and 11-of-15 at the free-throw line for fifth-seeded Nicholls (14-14), which will play Northwestern State in Thursday's quarterfinals. T.J. Carpenter added 13 points and Liam Thomas had 12 rebounds.
For eighth-seeded Southeastern Louisiana (12-18), Dre Evans scored in 15 points, Jeffery Ricard netted 11 and Antonnio Benton tallied 10 points and nine boards.
Southeastern shot 50 percent from the field in the opening stanza compared to 40.6 percent for Nicholls, but the Colonels attempted 12 more field goals than the Lions and the score was tied at 35 at the half.
The Colonels took the lead for good following a Luke Doyle 3-pointer with 11:28 left and pulled away later in the frame with an 8-0 run.
The Lions were plagued by a game-high 14 turnovers, which the Colonels turned into 30 points.