Heading to Campbelltown Stadium amid an injury crisis and with just a single win in their past seven games, the Phoenix's three points came at a pivotal time, lifting them back within four points of the top six.
"We've had a very up and down seven weeks now," Phoenix boss Giancarlo Italiano told Paramount.
"I've got enough stories to write a book.
"Proud of the effort with the players available. They've shown some real character tonight.
But after shrugging off Liam Rose's early injury and taking the lead via Jake Hollman's 15th-minute strike, just how his side hadn't killed the game before Kazuki Nagasawa and Barbarouses put the visitors ahead will haunt Bulls coach Mile Sterjovski, given his side's plethora of chances.
The hosts fired in 30 shots to nine through the game but a combination of wayward finishing - sending less than a third of those attempts on target - and inspired keeping from Kelly-Heald denied them.
Macarthur dropped to sixth with the defeat via a goals-scored tiebreaker with Sydney.
The 19-year-old Kelly-Heald, playing just his second senior game, was credited with eight saves on the evening, including four in one frantic 40th-minute stretch in which he made a series of quickfire stops to ensure the deficit remained one.
"Credit to Macarthur, they were amazing," Kelly-Heald told Paramount.
"They got to put us under the pump early, got an early goal, and then put us under the pump again.
"Looking forward [at halftime], we were going to just put our head down, grind, and try and get a result.
"Very stoked we got the points."
The Bulls' profligacy was punished in the second half, first in the 65th minute when a superb backheel volley from Hideki Ishige set up Nagasawa to fire beyond Filip Kurto, netting his first ALM goal and tying the game up.
Not having had much to do to that point, the Polish keeper's night went from bad to worse four minutes later when he brought down Barbarouses and gave away a penalty, one the veteran attacker converted for his 100th A-League goal.
The 34-year-old became just the fourth player in A-League history to achieve the feat, joining Bruno Fornaroli, Besart Berisha, and Jamie Maclaren.
