Mile Sterjovski's men looked to be heading for their maiden loss of the season with less than 10 minutes to go at Campbelltown Sports Stadium on Monday.
But Jake Hollman drew the home side level in the 82nd minute before Davila popped up three minutes later to nestle the ball past Joe Gauci in the Adelaide goal for the winner.
The result moves Macarthur up to third on the table with the side yet to taste defeat through their opening seven matches ahead of Saturday's away trip to face Sydney FC.
The first half was played at a frenetic pace from the off and it wasn't long after kick-off that the healthy crowd had their first goal of the night.
A floating free-kick found Valere Germain and the French striker glanced it home to put the Bulls up after just eight minutes.
Germain was in the thick of the action and, after a collision with Nestory Irankunda, stood over the Adelaide teenager and gave him a spray.
It was water off a duck's back for Irankunda, who careered down the right flank soon after and was able to find Zach Clough, who turned in for the Reds.
Adelaide were level but not for long, Macarthur's Mexican maverick Davila playing a ball in behind a high line five minutes after Clough's equaliser for Matt Millar to latch onto.
Typically a wing-back, Millar has found his calling further up the pitch under Sterjovski and buried the ball past Gauci for his third straight goal in as many A-League Men starts.
Davila had the chance to give Macarthur a third with a close-range header before the break but he could only fire the ball into Gauci's arms.
It was a mistake that would prove costly with Giuseppe Bovalina heading the Reds level on the stroke of halftime.
After letting their lead slip twice, Macarthur were made to pay when Clough burst in behind to grab his second in the 53rd minute.
The Bulls struggled to mount any sort of challenge as the second half wore on but substitute Hollman turned up in the right place at the right time to draw them level.
Suddenly, Adelaide looked in trouble and as Macarthur pressed forward, Davila was able to poke the ball past Gauci and into the back of the net to give the Bulls three points.
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