The Gers were restricted to any clear cut chances in the first-half but Ryan Jack managed to break the deadlock four minutes after the interval.
Ojo then added a second with a delightful curled finish in his debut start for the Steven Gerrard's side.
Alfredo Morelos and Connor Goldson rounded out the emphatic victory.
Sheyi Ojo scored his third goal since his loan move to Rangers this evening pic.twitter.com/SHComDlboD
— The LFC Lowdown (@TheLFCLowdown) July 9, 2019