Stein Huysegems scored the only goal of the game with 15 minutes to play at AAMI Park on Friday as the Heart fans showed their discontent to their coach by chanting in the dying stages.
The Heart settled first early on and probed to find an opening, but the Phoenix still looked dangerous in attack with Carlos Hernandez finding space in front of the home defence.
After a couple of early David Williams' sights on goal, the Phoenix could have taken the lead with two clear opportunities before the 10th minute.
Jeremy Brockie found himself one-on-one with Heart goalkeeper Andrew Redmayne after Manny Muscat's long ball but screwed his shot well wide of the right post.
Hernandez looked likely to make something happen with the ball at his feet facing the Heart defence and after Albert Riera's superb defensive work to win back possession, the Costa Rican's shimmy and low shot slammed off the bottom of the upright.
Heart had the best chance of the first half with Jason Hoffman releasing Michael Mifsud down the right channel and his centre to Williams at the back post was somehow side-footed wide with plenty of the goal to aim at.
The Phoenix eventually broke the deadlock in the 75th minute as substitute Tyler Boyd eluded Aziz Behich and slid a cross into the six-yard box that Huysegems duly stabbed home.
Huysegems' winner prompted the home fans to chant 'Aloisi out' and 'you are getting sacked in the morning' as the Heart crashed to their 17th game without a win.
