Cameron Payne posted 15 points and six assists for Murray State (20-11), which will play a yet-to-be-determined opponent in the quarterfinals.
Jonathan Fairell tallied 14 points and 13 rebounds, Jarvis Williams also scored 14 and T.J. Sapp netted 10.
Justin Simmons scored a team-high 14 points for Omaha (17-15). Devin Patterson added 12 points, John Karhoff had 10 points before fouling out and Mike Rostampour hauled in 12 rebounds.
Omaha ran out to a 15-8 lead less than six minutes into the game but quickly lost control, as Murray State held a comfortable 47-34 advantage at the half. The Racers shot 54.3 percent from the field in the first half, compared to 43.8 percent for the Mavericks.
The Racers' advantage never dipped below double digits in the second half, and they used a 16-4 run late in the game to put a stamp on the dominating victory.
Murray State knocked down 15-of-18 at the free-throw line, while Omaha was only 8-of-15 from the stripe. The Racers also won the rebounding battle, 46-35.