The European champions could not add to their advantage after the break, though, and Bradford pulled a goal back late on through Eoin Doyle's penalty.
There was never any danger of a comeback from the Bantams, though, as Liverpool maintained their 100% start to pre-season in what was their final outing before embarking on their tour of the United States.
Liverpool quickly took control of possession and needed only 13 minutes to break the deadlock when Milner cut onto his right foot and went for goal from 25 yards, seeing his effort glance off the head of former Everton striker James Vaughan to divert it past his own keeper.
If there was any doubt about the scorer of the first, Milner made 100% sure of his second moments later by tucking a confident penalty into the bottom corner after Ryan Kent had been brought down by Sean Scannell inside the area.
League Two Bradford may have feared that the floodgates would open after two goals in less than two minutes, but they did not let their heads drop and slowly began to work their way into the match.
Liverpool saw powerful long-range efforts from Alex Oxlade-Chamberlain and Milner fly well off target, although there were bigger scares for the hosts too and only a fine one-handed stop from Richard O'Donnell denied Harry Wilson from converting after a neat exchange with Brewster.
Bradford had threatening moments of their own, though, and Ben Richards-Everton even had the ball in the back of the net shortly after the half-hour mark, only for his header to be ruled out for offside.
Vaughan came close with a header of his own moments later as Simon Mignolet pulled off a stunning save to turn it against the post, although Bradford would have again been denied by the linesman's flag had it crept over the line.
Liverpool's third arrived four minutes before half time as Brewster added to his brace against Tranmere Rovers with another poacher's finish, squeezing home a rebound from the tightest of angles after O'Donnell could only parry Oxlade-Chamberlain's initial effort.
There were wholesale changes on both sides at half time as Liverpool switched their entire outfield lineup, while Bradford brought on a completely different XI.
It was still the European champions that dominated proceedings, though, and Divock Origi had the first sight of goal in the second half when he fired wide while trying to bend his finish into the bottom far corner from just outside the area.
A teasing Curtis Jones delivery almost created a chance for Liam Millar shortly afterwards, but substitute keeper Sam Hornby got to the ball first and the Bradford shot-stopper thwarted the Liverpool man again after the hour mark.
Jones and Origi then both failed to truly trouble Hornby with efforts from outside the box as Liverpool struggled to turn their possession into genuine clear-cut chances.
The prospect of a comeback never looked on the cards for the League Two outfit, but it was enough for them to win the second half as Liverpool offered little in response during the closing stages.
Jurgen Klopp's side will now travel to the United States for the main part of their pre-season tour, which begins against Borussia Dortmund next Saturday.
BRADFORD FIRST-HALF XI: O'Donnell; Henley, Mellor, Richards-Everton (O'Connor 33'), Longridge; Patrick, Palmer, Akpan, Gibson, Scannell; Vaughan
BRADFORD SECOND-HALF XI: Hornby; Taylor, French, O'Connor, Riley, Wood, Doyle, Nortey, Divine, Ainsworth, Donaldson
LIVERPOOL FIRST-HALF XI: Mignolet; Clyne, Phillips, Lovren, Larouci; Oxlade-Chamberlain, Lallana, Milner; Wilson, Brewster, Kent
LIVERPOOL SECOND-HALF XI: Mignolet (Atherton 81'); Gomez, Hoever, Matip, Lewis; Woodburn, Fabinho, Jones; Duncan, Origi, Millar body check tags ::