In the defining penalty shootout, Sydney's Alex Wilkinson sprayed his shot wide before Melbourne's Carl Valeri and teammate Marco Rojas failed to convert.
Sydney's Johnny Warren Medal winner Milos Ninkovic slotted the sealer - the Sky Blues joining the Victory and Brisbane as three-time A-League champions.
"I wanted it so badly for the players, for all they have done this year," Arnold said.
"I'm never happy. I am happy that we have done it but next year I have to raise the standard even more."
Melbourne coach Kevin Muscat says his team didn't deserve to lose on the balance of play.
"I suppose that's life. And that's football," Muscat said.
"But it's gut-wrenching trying to find the words now to explain to the players how they have lost. They didn't deserve to lose."
Melbourne's Besart Berisha and Sydney's Rhyan Grant scored the goals during the initial 90 minutes.
Berisha gave Victory the lead in the 20th minute with a sublime goal that stunned Sydney's parochial 41,546-strong crowd.
The polarising frontman took possession about 25 metres from goal and toyed with Wilkinson as he ran at the Sydney defender.
After jinking this way, then that, Berisha coolly converted during an opening half punctuated by an all-in melee.
Tempers boiled over in the 34th minute when Ninkovic was taken down by a Leigh Broxham tackle.
Ninkovic's instant remonstration escalated in to a push and shove involving all players: three of them - Ninkovic, teammate Filip Holosko and Melbourne's James Troisi - were booked in the aftermath.
After trailing at halftime, Sydney were rewarded for a period of sustained pressure after substitute David Carney swung onto his right foot and fired a powerful shot.
Victory goalkeeper Lawrence Thomas got a glove on the shot and Berisha a slight nod as the ball sailed along the goal line, before Grant steamed in for a 69th minute tap-in.
With scores tied, the decider went to extra-time and Melbourne playmaker Troisi came centimetres from a winner - his crisp volley in the 107th minute struck the inside of the left-hand post.
Just three minutes later, Sky Blues stalwart Carney was brought down and tumbled into the box amid cries for a penalty, but the foul occurred centimetres outside the box.
Carney then butchered a gilt-edged chance when in time and space in the box before the penalty shootout.
- AAP
