Ings sealed the victory two minutes from time with his first Reds goal, after Milner had broken 67 minutes of deadlock in Australia with his second strike in as many games.
Milner also scored in the 2-1 comeback win over A-League opposition Brisbane Roar, and manager Brendan Rodgers made only three changes from Friday’s starting XI.
Brisbane Roar 1-2 Liverpool video highlights: Milner assists & scores in comeback win for Reds
Other 2015 arrivals also impressed for the Merseysiders, with Joe Gomez producing another assured display at left-back and Divock Origi proving a nuisance up front without providing a real goal threat.
After an uneventful first half, Liverpool went close twice in eight minutes before the hour as Jordon Ibe fired narrowly wide of the post and Dejan Lovren thumped a header into the ground and over.
Ibe had been Liverpool’s most lively player throughout, and it was from his low cross that Milner, flourishing in a central role, stretched to turn home the opening goal from six yards out.
A third win from three for Liverpool was secured when substitute Ings collected a through ball from full-back Nathaniel Clyne to round the Adelaide goalkeeper and apply a composed finish.
Premier League attendance stats:
New Man United squad numbers: Schweinsteiger, Depay, Darmian & Schneiderlin digits REVEALED
Benteke latest: Liverpool AGREE payment plan with Villa, medical DATE SET, Man Utd STILL in frame