| The No.7 finished off a rapid team move with a quarter of the match remaining, before Ings converted coolly in the closing minutes to clock up a third consecutive win for the Reds on their pre-season tour.
It was another successful evening in Australia all round, with 53,008 fans gathering together to watch Brendan Rodgers' side in action.
The boss made three changes to the team that defeated Brisbane Roar - Joe Allen, Jordon Ibe and Dejan Lovren replacing Lucas Leiva, Ings and Mamadou Sakho respectively.
A confident start to the encounter saw the Reds move the ball around with intent, attempting to break through the United defence with a series of short passes and flicks.
Divock Origi took a more individual route towards goal in the 10th minute, gliding into space on the left side of the box and blasting an effort over the crossbar at the near post.
Summer signing Joe Gomez has already done enough in pre-season to ensure he won't be heading out on loan, according to the manager, but another composed beginning to this tie - typified by an eye-catching turn away from trouble on the flank - emphasised his comfort.
With 20 minutes played, Origi collected Allen's pass with a diagonal run across the Adelaide backline and was frustrated to send his low effort too close to home goalkeeper Eugene Galekovic.
Ibe then tried his luck from a similar positon, although the winger's lack of balance as he struck meant it was another straightforward take for the United stopper.
Only Adelaide attacker Craig Goodwin will know for certain whether his corner shortly after the half-hour mark was meant as a shot or not, but the curler was dangerous enough to have Simon Mignolet moving quickly across goal in case.
Galekovic was called into action again when Friday's match-winner, Milner, unleashed a swerving strike from 20 yards, springing to his right in time to palm away.
Playing in an advanced central position, the No.7 was regularly an option for his teammates and his next drive cannoned into Origi, who couldn't react successfully to the loose ball.
Alberto Moreno took to the field in place of Gomez for the second half, which continued in the same manner as the first - with Liverpool firmly on the front foot.
Firstly, an inviting corner from captain Jordan Henderson was met by Lovren but the central defender's header down into the ground bounced up and over.
Ibe nodded his own try straight at the 'keeper, then danced into space on the edge of the area and pulled a driven hit wide of the far post, before Galekovic leapt left to punch away an Adam Lallana curler.
The custodian was helpless to prevent Milner from finding the target on 67 minutes, though.
Henderson spread play to the right hand side for Ibe, who wasted no time in squaring across the penalty area, where Milner avoided an offside flag to divert home with his left foot.
Tarek Elrich threatened to equalise within moments when he lashed a stunning blast from 25 yards that whistled narrowly the wrong side of the post from his point of view.
But the Reds secured the victory when Nathaniel Clyne strode forward from full-back and slipped in Ings, who calmly took a touch to the side of Galekovic and tapped home. Next stop, Kuala Lumpur.
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