After the Skyhawks (9-19, 5-10) led 33-19 with 4:35 left until halftime, the Racers (20-8, 10-5) battled back for a 40-40 tie with 14:46 remaining but were unable to gain the lead.
Murray State got within a point five times in the final 6 1/2 minutes, but Tennessee-Martin held on and kept alive its hopes for the eighth and final berth in the conference tournament.
The Skyhawks shot 42 percent (21 of 50) from the floor, including 50 percent (7 of 14) from 3-point range while holding Murray State to 38.5 percent (20 of 52) shooting, including 25 percent (5 of 20) from the perimeter.
Isaiah Canaan, now 23 points away from joining the Murray State 2,000-point club, had 31 points for the Racers.
After the Racers got on the board first, Tennessee-Martin took over. With 7:24 glowing on the clock, the Skyhawks led 21-17, and they increased their margin to 30-19 on Dee Oldham's 3-pointer with just over 5 minutes left in the half.
Liabo's second trey gave Tennessee-Martin a 14-point lead, its biggest against Murray State in more than 11 years, and they led 36-27 at halftime. The Racers were 0 for 9 on 3-pointers in the first half, while the Skyhawks made 6 of 10 (60 percent).
Coming out of the break Canaan made his first 3 of the game to bring the Racers within seven points less than a minute into the second half.
A 7-0 run that included two baskets by Canaan, a Brandon Garrett layup and another Canaan 3 tied the game at 40 with 14:41 on the clock.
Murray State got back into it and called a timeout with 3 minutes on the clock, but coming out of the huddle, Canaan missed a 3-point attempt that would have tied the game.
Ed Daniel's layup and free throw with 2:13 left made it a two-point game, 64-62, and took Tennessee-Martin's Taylor out of the game with his fifth foul. But Daniel was unable to connect on either of two free throws 33 seconds later that could have tied the game, as Murray State coach Steve Prohm crouched on the sideline and looked at the ground.
Canaan hit his fifth 3-pointer of the night on an assist by Jeffery Moss with 1:02 on the clock to make the score 67-65.
A shot clock violation by Tennessee-Martin gave the Racers the ball with 22.9 seconds left. Canaan missed a layup attempt and Daniel was fouled while getting the rebound.
Daniel went to the line and missed both free throws, but a Skyhawks lane violation gave him another chance, and he put the Racers within one point with 8.6 seconds remaining.
Less than a second later, Liabo went to the line after being fouled by Canaan and made both free throws to seal the win for the Skyhawks.