Litton was 21-of-34 passing for 233 yards, Yurachek had six receptions for 77 yards and Keion Davis had 20 carries for 93 yards and a touchdown for Marshall (3-1).
The Thundering Herd scored touchdowns nine seconds apart to take control late in the first half. Litton found Willie Johnson for a 27-yard touchdown to cap a 10-play, 68-yard drive with 1:38 remaining in the second quarter. Artis Johnson forced a Thomas Geddis fumble on the ensuing kickoff return and Nazeeh Johnson recovered at the Cincinnati 15. Litton hit Yurachek on the next play to make it 24-0.
A 2-yard touchdown run by Cincinnati's Gerrid Doaks capped a 15-play, 75-yard drive to open the second half.
Cincinnati (2-3) fumbled a punt and, on the next play, Litton connected with Yurachek for a 31-yard score to give Marshall a 31-7 lead with 1:06 remaining in the third quarter.
Moore was 22-of-45 passing for 211 yards, including an 18-yard touchdown pass to Javon Hawes, but 13 of his completions came in the fourth quarter when Marshall played prevent defense.