Haskins completed 21 of 24 passes for 304 yards and five touchdowns. Two of his scoring tosses went to Campbell, who finished with eight catches for 147 yards.
Binjimin Victor, Terry McLaurin and Austin Mack also had touchdown catches for Ohio State.
Making only his fourth start, Haskins logged his third 300-yard game. That moved him into a tie with Troy Smith and Art Schlichter for second-most in Ohio State history. The record (eight) is shared by Joe Germaine and J.T. Barrett.
Tate Martell also led a scoring drive in the first half for the Buckeyes. That was capped by an 8-yard touchdown run by J.K. Dobbins, who finished the day with 55 yards on 11 carries.
PHOTOS: Meyer makes his return
Tulane’s first defensive stop came on the first possession of the second half against Ohio State’s second-team offense.
The Green Wave avoided a shutout with Darius Bradwell’s 2-yard touchdown run in the second quarter. That was set up by a 38-yard pass play from Jonathan Banks to Terren Encalade.
The Ohio State defense had eight tackles for loss in the first half and added six more in the second half despite substituting heavily.
Dante Booker led the way with three tackles for loss while Dre’Mont Jones and Baron Browning had 1.5 apiece. Jordan Fuller, Jashon Cornell, Isaiah Pryor, Chase Young, Justin Hilliard, Davon Hamilton, Keandre Jones, and Tyler Friday also recorded TFLs.
On the downside for the Buckeyes, running back Mike Weber left the game in the second quarter with what appeared to be an ankle injury. He limped off the field after a Tulane defender inadvertently rolled over his right foot at the end of a run.
Meyer was suspended after an independent investigation found he had mismanaged the employment of former receivers coach Zach Smith.