Blankenship scored from two yards out the put the Bobcats (2-1) up 31-17 early in the fourth.
The Thundering Herd (2-1) came right back as Rakeem Cato threw a 38-yard touchdown to Gator Hoskins, then forced Ohio to punt on the ensuing drive, but Cato was intercepted by Devin Bass on the next play.
Following a field goal by Ohio, Cato rushed for a touchdown to cut the deficit to three, but the following onside kick was recovered by the Bobcats to seal the game.
Tettleton was 25-for-38 with a touchdown and Matt Waters had 83 yards on six receptions.
Cato finished 30 of 44 for 367 yards for Marshall.
Tommy Shuler caught 9 passes for 95 yards receiving while Hoskins had 81.