Marshall had 25 carries for 203 yards for the Thundering Herd (3-1, 1-0), and also completed a pass for 27 yards.
With the Tigers (1-3, 0-1) leading 7-3 after the opening quarter, Marshall ran for touchdowns of 2 and 69 yards to take a 17-7 lead late in the second.
Matt Reagan kicked a 20-yard field goal to end the first half, then started the second with a 22-yarder to bring Memphis back within 17-13. Marshall ran it in from 5 yards out to give the Herd a 24-13 advantage to start the fourth. Craig Ratanamorn kicked an 18-yard field goal to seal the win for Marshall.
Tyler Bass was 17-for-34 passing for 232 yards, a touchdown and two interceptions for the Tigers. He also rushed for 64 yards on 14 carries.