The hosts increased their lead when Brandon Borrello found the net in the 38th minute, before Antonsson got his second shortly before the end of the first half.
Veteran Milos Ninkovic also got in the goalscoring act in the 53rd minute with Borrello secured his brace just three minutes later. Zach Clough scored a consolation goal for United in the 81st minute.
The Melbourne Knights also advanced by eliminating Campbelltown City 2-0, goals from Mohammed Sumaoro and Mitch Hore securing their berth in the last eight.
The hosts proved too strong for City, easily dominating in shots on target and possession at Knights Stadium.
It was a much more even contest at T.K. Shutter Reserve in Adelaide between MetroStars SC and Inter Lions FC.
The teams were goalless until Stars' Ren Nagamatsu broke the deadlock in the 92nd minute to break the Lions' hearts.
The winning trio join Brisbane Roar, who thumped Sydney United 5-0 on Saturday, in the Australia Cup quarterfinals.