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.
TCU had a lot to overcome, from torrential rains to an ankle injury that slowed Trevone Boykin, but the Horned Frogs dug deep to knock off Baylor.
Check out highlights from TCU's 28-21 double-overtime win over Baylor.
In a game that was marked by inclement weather, TCU prevails for the victory over Baylor in double overtime.
SEC Nation previews the Ole Miss vs. Mississippi State matchup.
SEC Nation previews the matchup between in-state rivals Florida and Florida State.
Players and coaches from Alabama and Auburn discuss the tradition of the Iron Bowl and the 2015 matchup.