England midfielder Milner got onto the end of Jordon Ibe’s cross to convert after 67 minutes – from what appeared to be an offside position – before substitute Ings rounded the keeper to double their lead late on.
It was an otherwise patchy display from the Reds, as they recorded their third win in a row after previously beating Thai All-Stars and Brisbane Roar.
Brendan Rodgers made three changes from the side that beat Brisbane Roar 2-1 in their last pre-season encounter, with Dejan Lovren, Joe Allen and Ibe coming in, while Mamadou Sakho, Lucas and Danny Ings dropped out.
A rousing rendition of ‘You’ll Never Walk Alone’ before kick-off failed to stir the players into a fast start, however, as both teams began in fairly laboured fashion.
Adam Lallana and Ibe were among those attempting to probe early on, with the latter finding himself with the ball at his feet in the box a couple of times but failing to really trouble Eugene Galekovic in the Adelaide goal.
Divock Origi, playing somewhat in the shadow of his Belgian team-mate Christian Benteke who could soon arrive at Anfield, was also guilty of not making more of a couple of first-half opportunities that came his way – firing tamely at the Adelaide keeper with one before failing to turn sharply enough onto another.
Liverpool kept coming forward but there was far too much loose attacking play in the final third to break the deadlock in the first 45 minutes.
Rodgers made just a single change at the interval, with Alberto Moreno replacing Joe Gomez at left-back, but it was down the right where Liverpool looked at their most dangerous, with Nathaniel Clyne and Ibe combining well to threaten the Adelaide defence.
First the former fired a dangerous ball across the face of goal, which no Liverpool player could get on the end of, before Ibe drove at two defenders before firing a shot just wide of the left-hand post.
Liverpool were getting closer, and Lallana brought the first real save out of Galekovic on the hour-mark, stinging the palms of the Aussie keeper with a fierce effort from the edge of the box.
Finally, after 67 minutes had passed, Liverpool finally broke the deadlock through Milner, but there was some controversy about the goal as the England midfielder appeared to be in an offside position when Ibe crossed for him to slide in and convert.
That was to take nothing away from the build-up, though, with Jordan Henderson superbly sliding the ball into the path of youngster Ibe – who was Liverpool’s best player on the day – before his perfectly-weighted ball found goalscorer Milner.
A throng of changes from both managers broke up play towards the end, and it was one of those substitutes in the shape of Ings, who made it two with his first goal in a Liverpool shirt.
Clyne drove forward and fed the former Burnley man, who picked it up calmly before taking the ball away from the keeper and converting calmly.
2-0 and job done for Liverpool. Not the best display but Rodgers will still be pleased as his side kept up their winning start to pre-season in front of a packed house at the Adelaide Oval.