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.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
Graduate transfer quarterback Davis Webb has officially joined California, giving the Golden Bears an experienced option to replace No. 1 overall NFL draft pick Jared Goff.
First-year football coach Dino Babers, hired by former Syracuse AD Mark Coyle, is on the committee that will search for Coyle's replacement.
Hugh Freeze has some major holes to fill on offense with the departures of Laremy Tunsil and Laquon Treadwell, but there is Chady Kelly and good depth.
After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.
The destination for Week 6 of the Big 12 Ultimate Road Trip is unanimous, as all three conference reporters would head to the Red River Rivalry.