Opening the competition's inaugural Unite Round with a bang, Davila grabbed a hat-trick for the Bulls at CommBank Stadium in Sydney.
But their slack defending repeatedly let them down, with Western United forward Daniel Penha causing particular problems in Friday's helter-skelter thriller.
Daniel Penha (left) celebrates after scoring what he thought was a late winner for Western United. (Dan Himbrechts/AAP PHOTOS)
Mile Sterjovski's Macarthur have not won in their last six after starting the campaign in blistering form.
Bottom of the table United secured a valuable draw - their first of a season that has yielded only two wins from 12 games - but John Aloisi's men will be kicking themselves for twice letting the lead slip.
United began with purpose, bursting down the right flank inside the opening two minutes with Brazilian import Penha heavily involved.
A whipped cross missed Matthew Grimaldi and Macarthur's Matt Jurman, with Ben Garuccio racing in at the back post to tuck the ball past Filip Kurto and put Aloisi's side 1-0 up.
The Bulls were struggling to get out of their own half but when they did it was through the efforts of Davila.
The 32-year-old had little to show for his early forays forward but managed to find himself in space with 32 minutes gone, taking one touch and dispatching a long-range rocket past Tom Heward-Belle to draw Macarthur level.
Michael Ruhs goes close for Western United in their thrilling 3-3 ALM draw with Macarthur FC. (Dan Himbrechts/AAP PHOTOS)
The Bulls skipper was on the receiving end of some heavy Western United challenges but continued to surge forward with the ball, adding his second soon after the halftime break.
Dispossessing Angus Thurgate in the Bulls' half, Davila charged upfield with the ball, squeezing past two covering defenders.
Teammate Jake Hollman was unable to control a pass towards the edge of the box and defender Josh Risdon looked to have nipped the attack in the bud.
But the ball got caught under Risdon's feet, and as Davila pressed him a backpass towards Tomoki Imai only encouraged the Mexican midfielder, who nabbed the ball back inside the box.
Davila calmly rounded Heward-Belle to put his side in front.
Macarthur now looked more assured but when a Thurgate rocket rattled the bar with 74 minutes gone, Penha was on hand to turn the ball in.
With the scores level, United grew with confidence and Penha put them ahead with a powerful effort from outside the box with five minutes left.
Coach Aloisi skipped down the touchline with glee, but his delight was short-lived when Davila flicked home a header in the 90th minute to grab a point for the Bulls.
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