The England international netted his second goal in successive friendlies after he broke the deadlock with 15 minutes remaining in Australia.
Milner, who joined in a free transfer from Manchester City earlier this month, had also bagged a strike against Brisbane Roar in their previous outing on their pre-season tour of Asia and Australia.
His compatriot Ings, who moved to Liverpool from Burnley after an impressive first season in the Premier League, sealed the win in the final moments of the game.
New Liverpool signing Divock Origi came close to scoring against Adelaide but the Belgium international couldn’t beat home goalkeeper Eugene Galekovic.
Meanwhile, another new arrival, Joe Gomez, impressed in the defence again after Brendan Rodgers revealed that the youngster won’t be going out on loan following his move from Charlton Athletic.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news