Wayne graduate Robert Landers crashed into the backfield and dragged Raheem Blackshear down for a 3-yard loss on the first play of the game, a sign of things to come.
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The Scarlet Knights punted three plays later, and Ohio State promptly drove 67 yards for a touchdown in less than two minutes.
Dwayne Haskins capped the drive by finding Johnnie Dixon with a beautiful deep ball for a 38-yard score and the rout was on.
Haskins threw two more touchdown passes before the half was up, and backup Tate Martell connected on one, too.
A J.K. Dobbins 2-yard run with five minutes on the clock made it 35-0.
By the time the Ohio State Marching Band took the field to perform a tribute to The Blues Brothers, it was all over but the shouting.
The Buckeyes, who beat Oregon State 77-31 a week ago, tacked on another touchdown to start the third quarter when Haskins hooked up with Dixon from 44 yards out.
Later Martell found the end zone himself, scampering 47 yards for a touchdown midway through the fourth quarter.
Ohio State also got a 21-yard field goal from Sean Nuernberger.
Rutgers got on the board with a 41-yard field goal by Justin Davidovicz with 8:02 left in the third quarter. Those were the Scarlet Knights’ first points against Ohio State since the fourth quarter of the 2015 game, snapping a scoreless streak of 10 quarters.
Haskins finished the day 20 for 23 for 233 yards and four touchdowns.
Parris Campbell caught five passes for 64 yards and a touchdown while Dixon had 89 yards and two scores on four catches.
Luke Farrell and Terry McLaurin also had touchdown catches for Ohio State in the first half.
Dobbins ran for 73 yards on 12 carries.
Martell completed all 10 of his attempts, good for 121 yards, and added 95 yards rushing.
Nick Bosa led the defensive charge, notching five tackles, including a sack.
Ohio State outgained the Scarlet Knights 579-134, including 310-45 in the first half.
Next up for the Buckeyes is a trip to Arlington, Texas, where they will take on No. 16 TCU next Saturday night.