Liverpool destroyed Lincoln City with a 7-2 victory in the EFL Cup third-round on Thursday.
A double from teenager Curtis Jones made it 3-0 before half-time, with Minamino scoring just a minute after the break.
Tayo Edun pulled one back for the League One outfit but Marko Grujic quickly restored the five-goal advantage.
Lewis Montsma then scored for Lincoln and Divock Origi got the Reds' seventh.
Diogo Jota, signed from Wolves last week, made his debut as a second-half substitute.
Reds boss Jurgen Klopp handed starts for teenagers Jones, Harvey Elliot, Rhys Williams and Neco Williams.
Kostas Tsimikas also got his first start for the club, but fellow signing Thiago was left out of the match-day squad.
"They deserved their two goals," Klopp told BBC Radio 5 Live.
"We played a really good football game tonight. It was easy on the eye. We passed the ball and finished situations off. The boys wanted to play football and showed an exceptional attitude.
"That's how it should be [Liverpool's second XI playing like their first]. Wear the shirt and show who you are. I'm happy with everything.
"Two goals we conceded were not nice, but it's not a massive problem. You can have struggles in a game like this."