The Reds used the match with their Merseyside neighbours as a chance to field two entirely different lineups either side of half time.
Brewster scored twice during his 45 minutes on the field with a couple of poachers' finishes after Nathaniel Clyne had opened the scoring early on at Prenton Park.
Liverpool were ahead with less than six minutes played as Clyne hammered the ball past Scott Davies after being teed up by Brewster 15 yards out.
Davies produced a couple of stops to deny Yasser Larouci - the first a straightforward save down the middle and the second a good save down low.
Tranmere had a couple of lively moments in the first half as Corey Blackett-Taylor twice tested Simon Mignolet, yet they found themselves three goals down at the interval as Brewster again reacted quickest to fire home after Milner's latest long-ranger was parried.
Liverpool required less than 10 minutes of the second period to add to their goals tally, with Jones converting at the back post after getting on the end of a floated cross from Ben Woodburn.
Second-half captain Origi made it five by brilliantly controlling a long ball from Joel Matip and rounding the keeper.
Tranmere struggled to get anywhere near their opponents and they were six goals down with 22 minutes left when Duncan profited from some poor defending to convert following some good work from Ki-Jana Hoever.
TRANMERE ROVERS (4-2-3-1): Davies; Caprice, Ray (Gilmour 46'), Monthe (Spellman 85'), Ridehalgh (Woods 46'); Banks (Payne 46'), Perkins (Nelson 46'); Morris (Ponticelli 46'), Jennings (Miller 46'), Blackett-Taylor; Mullin (Potter 46')
LIVERPOOL FIRST-HALF XI (4-3-3): Mignolet; Clyne, Phillips, Gomez, Larouci; Oxlade-Chamberlain, Milner, Lallana; Wilson, Brewster, Kent
LIVERPOOL SECOND-HALF XI (4-3-3): Jaros; Hoever, Matip, Johnston, Lewis; Woodburn, Fabinho, Jones; Glatzel (Atherton 77'), Origi, Duncan