Van Dijk put Adelaide in front after 37 minutes when Simon Colosimo brought down Bruce Djite in the box and the Dutchman beat keeper Clint Bolton from the spot.
The visitors doubled their advantage two minutes after the break when van Dijk and Zenon Caravella combined to present Dario Vidosic with an opportunity in the box that he duly accepted.
Van Dijk then sealed the points for John Kosmina's side in the 79th minute with a powerful finish before Eli Babalj produced a fine consolation effort for Melbourne on the stroke of full-time.
Gold Coast United remain bottom of the table after a spirited fightback was thwarted in a 3-2 defeat to Newcastle Jets at Ausgrid Stadium.
Jeremy Brockie broke the deadlock with a header from Nikolai Topor-Stanley's cross two minutes before the interval and grabbed his and Newcastle's second in the 64th minute when he brought down Ryan Griffiths' pass and found the back of the net.
Gold Coast battled back through Ben Halloran's first-time strike and Adama Traore's goal but substitute Labinot Haliti fired home the winner 11 minutes from time.
Two late goals saw Wellington Phoenix come out on top 4-2 against Sydney FC at Westpac Stadium.
Sydney took the lead after 15 minutes when Vince Lia was penalised for handling in the box and Brett Emerton converted, but the hosts drew level nine minutes later when Jamie Coyne committed the same offence and Daniel Cortes made no mistake from the spot.
Wellington then went in front four minutes before the break when Dani Sanchez chipped Sydney keeper Liam Reddy but Bruno Cazarine levelled in the 63rd minute after being sent clear by Emerton.
Phoenix regained their advantage with 13 minutes remaining when Ben Sigmund headed home Leo Bertos' corner and Paul Ifill wrapped up the points in stoppage time with the substitute firing into the bottom corner.
Central Coast Mariners extended their lead at the top to six points as Matt Simon scored in each half to down Melbourne Victory at Bluetongue Stadium.
Simon, playing his last game for the club before moving to Korean side Chunnam Dragons, opened the scoring after just 20 seconds when he converted Troy Hearfield's cross.
Bernie Ibini-Isei hit the post for the hosts in the second-half before Simon capped a memorable farewell with his second of the game in the 84th minute.
Brisbane Roar climbed to second on goal difference after they were held to a 3-3 draw at Perth Glory.
The hosts established a two-goal advantage when Billy Mehmet set up Travis Dodd with 16 minutes gone at nib Stadium before Mile Sterjovski lashed home a 20-yard drive eight minutes later.
However, Brisbane replied with two goals shortly before half-time. First, Mitch Nichols reduced the arrears in the 40th minute with a shot from the edge of the box and Erik Paartalu then nodded in Luke Brattan's corner.
They then went in front midway through the second period when Nichols latched onto Paartalu's ball over the top and he chipped keeper Danny Vukovic.
Perth, though, earned a share of the spoils with 10 minutes to go when Ivan Franjic fouled Sterjovski in the box and the latter held his nerve to fire home the penalty.