The Bulls led 2-0 after just 10 minutes before finding themselves 3-2 down at half time.
Two goals soon after the interval had them leading 4-3 before United equalised for the second time with 20 minutes remaining.
But, skipper Luke Brattan scored his second with a delightful free kick on 83 minutes which proved the winner.
Macarthur made the perfect start and caught Adelaide napping on eight minutes.
Keeley Adamson whipped in a deep cross from the right that looked to have evaded everyone, but Marin Jakolis kept the ball in and volleyed back across the face of goal for Chris Ikonomidis, who ghosted in at speed to tuck the ball away.
Two minutes later the visitors doubled their lead after the Reds played themselves into trouble in defence.
With his side committed to passing their way through Macarthur's high press, Bart Vriends played a central ball to Ethan Alagich, who was unable to control under pressure.
Jake Hollman took possession and squared a pass which was partially cleared with the loose ball sitting perfectly for Adamson who unleashed with a half volleyed from just inside the area.
United pulled a goal back on 13 minutes when Stefan Mauk slipped through Zach Clough who drilled it across the face of goal to find Austin Ayoubi at the back post to tap in from close range.
The goal sparked Adelaide to life and the home side was level in the 19th minute. Mauk teed up Ryan Kitto, who let fly with a stunning left-footed strike from 25 metres that gave Filip Kurto no chance as it ruffled the top corner.
United' first half comeback continued with another impressive goal on 42 minutes, this time from Mauk.
On halfway, Hollman lumped the ball 30 metres in the wrong direction, causing confusion between team-mates Tomi Uskok and Yianni Niccolaou. The latter attempted to take possession but was robbed by Ayoubi, who laid off to Mauk.
The Reds' midfielder took a touch before looping his shot from 20 metres over Kurto.
Adelaide had two more chances before the break. Archie Goodwin blasted over from five metres out after a superb run from Harry Crawford before Kitto had the ball in the back of the net in first half injury time, but it was ruled out for an offside in the lead up.
United would rue the squandered opportunities as Macarthur levelled on 53 minutes with Adelaide again their own worst enemy.
Goalkeeper James Delianov's pass was intercepted by Ikonomidis and eventually found its way to Luke Brattan at the top of the box, who powered his shot low and hard down the middle.
Four minutes later, the visitors were back in front. Substitute Peter Makrillos danced past a couple of Reds defenders on the edge of the area before threading a pass for Jakolis who fired past Delianov from 12 metres.
Goodwin atoned for his first half error when he made it 4-4 on 73 minutes. Like Delianov minutes earlier, Kurto misplaced a pass out of defence which went straight to Mauk, who squared for Goodwin to rolled the ball into an unguarded net.
United's joy was short-lived as Brattan grabbed his second. The Macarthur skipper sized up a free kick on the edge of Adelaide's penalty area before lifting it over the wall and into the bottom corner.
The Reds thought they had equalised on 90 minutes when substitute Luka Jovanovic found the net, but it was ruled out for offside.
Fellow substitute Yaya Dukuly rattled the upright in stoppage time, with the post denying Adelaide once more.
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