Marshall, who had missed the previous four games with a knee injury, came off the bench to make 5-of-11 shots and 9-of-10 at the foul line and lead MSU's efforts. Jarmar Gulley added 15 points, while Christian Kirk scored 12 off the bench with a team-high 6 rebounds.
ORU (5-5) was led by Shawn Glover who tallied 16 points, while Brandon Conley added 16 points and 6 boards.
The Bears showed poise and maturity down the stretch to earn the victory, as Marshall and Gulley teamed up to break a 52-52 tie with under four minutes to go. Marshall's free throw and Gulley's driving layup pushed the visitors back ahead 55-52 with 3:01 on the clock.
With the Golden Eagles in the double bonus, Glover knocked down a pair of free throws to make it a one-point game with 2:40 to play, but Gulley's scoop shot at the rim soon gave MSU a 57-54 advantage.
Oral Roberts would cut the deficit to one once more, but Marshall's fade-away 20-footer with 1:19 remaining was the beginning of the end for the home club. Gulley scored a traditional 3-point play with 43 seconds to go after a miss by Korey Billbury to give Paul Lusk's squad a 62-56 advantage.
MSU refused to foul with the Golden Eagles in desperation mode, leading to a dunk back by Conley and a pair of 3-pointers. But MSU was dead on from the foul line down the stretch, making eight straight after Gulley's 3-point play to seal the win.
MSU finished 16-of-18 (.889) at the foul line and 25-of-58 (.431) from the field with 4-of-12 (.333) makes beyond the arc.
ORU out-rebounded the Bears, 33-31, but the Golden Eagles had just two offensive rebounds. Scott Sutton's squad was 23-of-49 (.469) from the field, 8-of-17 (.471) from long range and 13-of-20 (.650) at the line with 13 turnovers.
The Bears came out on fire to start the second half as a left-hander by Emmanuel Addo and a 3-pointer by Austin Ruder gave MSU a 33-26 advantage with just over two minutes expired in the second period. After ORU cut the Bears' lead to three, Missouri State went on a 9-3 run to take their biggest advantage of the night, 44-35, after a short jumper off the glass by Kirk and traditional 3-point play by Gulley gave MSU a 44-35 advantage at the 13:10 mark.
But just over eight minutes later, the game was tied, giving the visiting Bears a chance to shine in the clutch.
In the first half, the Bears overcame an early five-point deficit to lead 26-24 at the intermission as Marshall
kissed one off the glass just before the horn.
MSU overcame a 4-for-14 start from the field with a key 8-0 run over a two-minute span late in the half. Back-to-back 3-pointers by Marshall and Gavin Thurman set up a put-back by Kirk to give MSU a 21-18 lead with 6:24 on the clock.
ORU responded with a five-point outburst of its own to retake the lead briefly, but a try from freshman Ruder pushed
the visitors back on top 24-23. ORU added a free throw with just over a minute to go before the go-ahead bucket by Marshall going into the break.
MSU heads to defending national champion Louisville on Dec. 17 for an 8 p.m. (Central) tipoff from the KFC YUM! Center in Louisville, Ky. The Bears are home again on Dec. 21 against Alabama A&M at 7:05 p.m.