A frenetic opening half produced five goals, a straight red card to Sydney defender Marc Warren and an Alessandro Del Piero penalty on the night of his 39th birthday.
Del Piero's spot kick proved the difference in the end, killing a three-match ending streak that had seen Farina's position under threat.
Richard Garcia put the hosts ahead before a freak goal from Seb Ryall doubled the lead as Melbourne defender Jason Geria's clearing header hit him in the face and ended up over the line.
Archie Thompson pulled a goal back for Victory in the 17th minute and home nerves were further frayed as Warren was dismissed for felling a goal-bound Connor Pain.
From the resulting free-kick, James Troisi netted a deflected effort as the pressure mounted further on Farina.
However, Del Piero picked himself up after being fouled in the area to slot home the winner in a breathless encounter.
Elsewhere, Newcastle Jets grabbed their first win of the season with a hard-fought 2-1 victory over Adelaide United at Coopers Stadium.
Two strikes either side of the half-time interval, through Kew Jaliens and Adam Taggart respectively, enabled the Jets to build the foundation on which they earned their triumph.
Adelaide got one back courtesy of Fabio Ferreira's header in the 71st minute but they found it an impossible task to steal a last-ditch draw with just 10 men after Nigel Boogaard's 90th-minute red card.
Wellington Phoenix are still searching for their first win of the A-League season - and their first under coach Ernie Merrick - after holding on for a 1-1 draw with Perth Glory in Christchurch.
The early signs were good for the home side when skipper Andrew Durante bundled the ball over the line after just four minutes.
But Glory got on top as the half wore on and grabbed a deserved equaliser through Ryo Nagai 25 minutes later.
Both sides had their chances to claim all three points in the second half but lacked the poise and finish in front of goal.
