For the second time in four days, the Premier League club attracted a big crowd to an Australian stadium and were given a good workout by A-League opposition.
And as in their 2-1 win over Brisbane Roar on Friday, Milner impressed in central midfield and got on the scoresheet, breaking the deadlock in the 68th minute by guiding Jordan Ibe's cross into the net from what looked like an offside position.
Ings scored the second goal three minutes from time after being put through on goal by England international Nathaniel Clyne.
Ibe put in an impressive display on the right wing in front of 53,008 fans at the Adelaide Oval and had been involved in two good chances around the hour mark.
First he cut inside the box and shot just wide of the post and a minute later provided a well-judged pass for Adam Lallana's shot, only for Adelaide goalkeeper Eugene Galekovic to produce an outstanding save to keep the match goalless.
"Jordan Ibe, I think this could be a big season for him and he's only 19," said Liverpool manager Brendan Rodgers.
"I thought it was an excellent performance. We pressed the game really well against a good side and we're really happy with the performance and the fitness."
If Ibe was impressive, Divock Origi gave a reminder of why Liverpool are reported to be on the verge of spending 32.5 million pounds ($50.73 million) on another Belgian striker in Christian Benteke.
Origi was free in front of goal when he failed to get on the end of a Joe Gomez cross in the fifth minute and that was only the first of a string of missed opportunities.
Gomez, 18, impressed Rodgers with another assured display at right back, even if Spanish winger Sergio Cirio gave him some trouble in defence.
"Young Joe Gomez, looks like he could be a Liverpool player for a number of years," Rodgers added. "I know it's pre-season but he shows all the qualities and temperament."
Tarek Elrich, who scored the A-League goal of the season in the last campaign with a brilliant individual effort, created Adelaide's best chance in the 72nd minute when he did well to win the ball but fired his shot onto the outside of the post.
(Reporting by Nick Mulvenney in Sydney, editing by Amlan Chakraborty)
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