The drive was kept alive when Haskins hit tight end Rashod Berry to convert a fourth-and-1.
Maryland wasted no time on its possession as Anthony McFarland went 24 yards on the first play. It was ruled a touchdown initially, but a review found his knew was down at the 1.
The Terrapins scored one play later anyway, then interim coach Matt Canada opted to go for the win rather than tie the game with a PAT kick.
He was not rewarded as quarterback Tyrrell Pigrome missed an open receiver in the end zone.
Haskins finished the afternoon with 405 yards passing. He threw three touchdown passes and ran for three touchdowns playing in front of friends and family in the state where he attended high school.
Terry McLaurin had four catches for 118 yards and a touchdown while Johnnie Dixon added 102 yards on six catches for the Buckeyes.
J.K. Dobbins ran for 203 yards on 37 carries and scored a touchdown as Ohio State won despite giving up 535 total yards, including 339 on the ground.
McFarland accounted for 298 of those yards on just 21 carries. He averaged 14.2 yards per carry.
Maryland leads Ohio State 24-17 at halftime of a wild game in College Park.
The Terrapins shredded the Buckeye defense throughout the first 30 minutes, starting on Maryland’s second play from scrimmage when Anthony McFarland went around left end for an 81-yard touchdown.
Roughly five minutes later, he torched the Buckeyes again, breaking a tackle just beyond the line of scrimmage and sprinting 75 yards for a score.
Maryland also set up a 36-yard field goal with a 56-yard pass from Tyrell Pigrome and got a 16-yard touchdown run by Javon Leake in building its lead.
The Terrapins ran for 281 yards in the first half, overshadowing a strong start for the Ohio State offense.
Ohio State had a chance to tie the game late in the quarter but J.K. Dobbins fumbled at about the 6-yard line and Maryland recovered in the end zone for a touchback.
That marred a great first half for Dobbins, who ran for 109 yards on 20 carries including a 1-yard touchdown.
Dwayne Haskins completed 10 of 12 passes for 198 yards for Ohio State, including a 68-yard touchdown pass to Terry McClaurin.
Haskins broke Joe Germaine’s single-season school record for passing yards on that play.