Alessandro Del Piero's first-half penalty and a tap-in from Joel Chianese saw Sydney to their first win at AAMI Park.
It marked their first victory away from home since December 2012 and moved Frank Farina's men into third in the A-League table.
The bottom-placed Heart are winless in six games this campaign and their run of outings without victory stretches to 11 matches, dating back to February.
Since taking over as coach in May 2012, Aloisi has led the Heart to just eight wins in 33 matches and is set to come under further pressure despite being recently backed by chief executive Scott Munn.
Sydney were the brighter side early on, but the Heart spurned a glorious chance after 14 minutes when Michael Mifsud blasted a shot straight at Vedran Janjetovic.
Del Piero clipped the crossbar with a free-kick after 21 minutes, only to open the scoring six minutes later after Chianese had been brought down in the penalty area by a sliding Rob Wielaert.
Chris Naumoff hit the post before Sydney added to their lead in first-half injury-time, Chianese converting from close range after good work from Ali Abbas down the left.
Melbourne were unable to respond and Sydney coasted to a second straight win.
