In a clash where the home team failed to register a single shot on target until the 93rd minute of the game, Sawyer's close-range finish in the 83rd minute was enough for the Bulls to claim their second win of the season and move above the Phoenix into seventh on the A-League ladder.
The breakthrough came when Macarthur captain Luke Brattan, a standout in midfield throughout, released the always dangerous Harry Politidis.
Sawyer got the ball ahead of Josh Oluwayemi in the Phoenix goal and bundled home for Macarthur's first away goal of the season.
It's the first time this season the Phoenix have failed to score and also extends an unwanted streak of 17 A-League Men matches without a clean sheet.
The Bulls got off to a bright start and thought they'd taken the lead in just the eighth minute but Matt Jurman's close-range finish was ruled out due the former Socceroo being deemed offside.
Oluwayemi made the first of three excellent stops on the half-hour when he pushed Ji Dong-Won's toe-poked effort around the post after clever hold-up play by Rafael Duran.
While the Phoenix were unable to trouble former Wellington goalkeeper Filip Kurto in the Macarthur goal in the opening 45, dangerous Nigerian forward Ifeanyi Eze threatened to add to his three goals this season with a chance right near halftime which just drifted wide of the goal.
After a cagey start to the second half, the Bulls fluffed a great chance to take the lead following a lightning counter-attack in the 60th minute.
Anthony Caceres' released Sime Grzan but the Croatian was denied one-on-one after another piece of excellent goalkeeping on the edge of the penalty area by Oluwayemi.
Wellington did get the ball in the back of the net in the 76th minute through Eze after Kazuki Nagasawa broke clear but just as with Jurman's effort in the opening half, the goal was ruled out when the Japanese midfielder was flagged for offside.
Phoenix defender Isaac Hughes then went desperately close to breaking the deadlock when his header from a Carlo Armiento free-kick flashed agonisingly past the far post in the 79th minute.
The frustration from that near miss was then compounded by Sawyer's late winner just a few minutes later.
There was still time for one more excellent save from Oluwayemi to deny Grzan again before the Phoenix finally tested Kurto in the 93rd minute with the Pole at full stretch to tip Armiento's long-range strike past the post and secure the points for the visitors.
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