Brewster, who missed the whole of last season through injury, scored both of his goals from inside the six-yard box after Nathaniel Clyne had opened the scoring early on.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
Less than six weeks on from lifting the Champions League in Madrid, the Reds are back in action with a short trip across the River Mersey for the fourth successive year.
The ultimate aim for Liverpool this season is to defender their European crown and end their long wait for a Premier League title, while opponents Tranmere are focusing on remaining in League One following their promotion in May.
STARTING XI: Mignolet; Clyne, Phillips, Gomez, Larouci; Oxlade-Chamberlain, Milner, Lallana; Wilson, Brewster, Kent
SUBS: Jaros, Atherton, Hoever, Matip, Johnston, Lewis, Fabinho, Jones, Woodburn, Duncan, Glatzel, Origi
STARTING XI: Davies; Caprice, Ray, Monthe, Ridehalgh; Bank, Perkins; Morris, Jennings, Blackett-Taylor; Mullin
SUBS: Pilling, Nelson, Thompson, Woods, Ponticelli, Gilmour, Miller, Spellman, Potter, Walker-Rice
Davies produced a couple of stops to deny 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 Blackett-Taylor twice tested 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.
TRANMERE SUBS: Pilling, Nelson, Thompson, Woods, Ponticelli, Gilmour, Miller, Spellman, Potter, Walker-Rice
Brewster, who missed the whole of last season through injury, scored both of his goals from inside the six-yard box after Clyne had opened the scoring early on.
The Reds changed their entire side for the second half and they scored another three goals after the restart, with Jones, Origi and Duncan adding their names to the scoresheet.