Leading 94-93, Chad Posthumus grabbed an offensive rebound off a miss by Turner and was fouled by Elijah Pittman. Posthumus converted two free throws to start a 10-1 run by the Eagles to close out the game.
Kareem Canty's 3-pointer with a minute left in the first half gave Marshall a 21-point lead, its biggest of the game, 48-27. Morehead State (3-1) closed the half with a 6-0 spurt to head into the break trailing 48-33.
The Eagles held 16-8 advantage on the offensive glass and outscored Marshall 21-3 in second-chance points.
Posthumus scored 14 points and pulled down 15 rebounds, seven offensive.
Elijah Pittman tied a career-high with 31 points for Marshall (2-1). Kareem Canty added 19 and nine assists but had nine turnovers.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
|Texas San Antonio||3-15||13||5-27|
|Southeast Missouri State||2-14||8||5-24|