Winless Heart needed a response at AAMI Park but they did not get it as the Sky Blues made it back-to-back wins against Melbourne opposition.
Alessandro Del Piero's first-half penalty and a tap-in from Joel Chianese saw the Sky Blues to their first ever win at AAMI Park.
It marked their first victory away from home since December 2012 and provisionally moved Frank Farina's men into third on 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 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 backed by chief executive Scott Munn.
Sydney were the brighter side early, but it was the Heart who created a glorious chance on 14 minutes.
Paulo Retre's header found Michael Mifsud in the area after Brett Emerton was too slow to push up after the Sky Blues cleared a corner.
But the Malta international lacked composure and failed to take the chance, blasting his shot straight at Vedran Janjetovic in a one-on-one.
Del Piero went close with a free-kick on 21 minutes as his dipping 20-yard effort clipped the crossbar with goalkeeper Andrew Redmayne beaten.
The Sky Blues continued to threaten before Chianese won his side a penalty on 25 minutes, brought down by a sliding Rob Wielaert on the left side of the area.
Del Piero stepped up and found the bottom corner, sending Redmayne the wrong way for his third goal of the season.
Chris Naumoff wasted a good chance as he struck the post and Nick Carle also squandered a glorious opportunity as Redmayne kept out his tame effort in another one-on-one.
Sydney found a second goal in first-half additional time in simple fashion as the Heart fell asleep before the interval.
Heart offered the wide areas to be exploited and Abbas took advantage down the left, sliding a pass across the face for Chianese, left unmarked by Aziz Behich, to tap into an open net.
The hosts lacked any real energy and despite putting on some pressure, it was Sydney who went close again on the hour-mark as Chianese pushed a shot wide from close range.
Behich had a powerful close-range strike saved soon after but Heart, who have now gone 390 minutes without a goal, struggled to create the chances they have without scoring in recent weeks.
Aloisi's men had a chance scrambled away late on as Golgol Mebrahtu was denied and Sydney coasted to a second straight victory.