Kosta Barbarouses (14), Archie Thompson (68) and Mitch Nichols (78) scored the goals as Melbourne survived a red card to Adrian Leijer just before half-time and a second-half penalty to pick up a third win of the campaign and climb to fourth place.
The game looked set for a significantly different conclusion with Melbourne leading 1-0 just after the hour mark, as Adelaide were awarded a penalty when Jeronimo Neumann went down in the box but Victory goalkeeper Nathan Coe saved Sergio Cirio's spot-kick.
Ranko Despotovic hit a late winner as Sydney FC claimed a 2-1 victory over Wellington.
Despotovic slotted home the crucial goal in the 94th minute to kill off the brave Phoenix and sweep the Sky Blues to third in the table.
Richard Garcia fired the hosts ahead on 35 minutes but they were then forced to play the final 20 minutes a man down after Pedj Bojic was sent off for a second bookable offence.
Sydney were hanging on for dear life when Wellington equalised through Kenny Cunningham a minute into time added on but Despotovic popped up to win it late on.
In the day's late game, Perth Glory suffered a last-gasp 2-1 loss at home to Central Coast Mariners.
Glory took the lead through Jamie Maclaren's well-taken lob after 25 minutes but the Mariners hit back through Michael McGlinchey 10 minutes later before Mitchell Duke claimed the winner in the closing moments.