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The hosts led through an early Patrick Kisnorbo goal, before conceding to Bruce Djite late in the first half.
David Villa, playing in what is likely to be his final match for City, nearly fashioned a goal out of nothing with an improbable, mesmerising dribble mid-way through the second half, but the Spanish star was unable to leave a parting gift for his temporary club.
Marcelo Carrusca's late penalty then sealed the win for the away side, leaving John van 't Schip and his players still searching for their first victory of 2014-15.
What they said
Djite: "Fantastic team effort. When you go 1-0 down away it's always very difficult, we knew that after we copped the goal early on. But we had the belief we could come back and we did that tonight. It's early in the season but it just shows we're showing some promise this season. We've got the ingredients, it's just baking the cake. Let's just wait and see."
Paartalu: "A new team put together takes time to gel. We're not putting in 90 minute shifts at the moment. It's just not good enough. We got a little bit stretched, maybe switched off a few times in the second half. We've got to mark better and be smarter."
Goals
1-0 (Kisnorbo 9')
Damien Duff's in-swinging corner was met by the head of captain Kisnorbo, who directed the ball to the far corner of the net, leaving Eugene Galekovic with no chance.
1-1 (Djite 39')
A sloppy lull descended on the game after the opener and when Adelaide's equaliser arrived, it came out of nowhere.
Fullback Ben Garrucio, on as a substitute for the injured Jonatan Germano, followed Awer Mabil inside and Tarek Elrich found himself with acres of space down the right, swinging an inviting cross into the penalty area.
Djite met it virtually unmarked, powering a header past Andrew Redmayne and in off the underside of the crossbar.
1-2 (Carrusca, penalty 79')
Garrucio's slip let in substitute Bruce Kamau and Redmayne was forced to bring the youngster down. Referee Chris Beath pointed to that spot and Carrusca stroked home the penalty with aplomb.
Key moment
Kisnorbo was lucky not to be sent off for denying an obvious goal-scoring opportunity just past the hour mark, picking up only a booking despite bringing down Djite with the Adelaide centre-forward bearing down on goal and Robbie Wielaert struggling to get across and cover. That narrow escape still wasn't enough for the home side to take anything out of the game.
Highlights reel
He embarrassed himself with a botched rabona in the first half but Carrusca almost made amends with 20 minutes to go, sending an audacious lob from close to the half-way line narrowly wide of goal with Redmayne beaten. The Argentine playmaker made no mistake from the spot with 10 minutes to go.
Coach killer
Garrucio won't be keen to watch back the video of Adelaide's equaliser. The youngster, with eyes only for the dangerous Mabil, was dragged badly out of position, leaving Elrich with all the time in the world to pick out Djite. It was his failure to deal with Isaias' pass to Kamau that led to Adelaide's winner. City's left-back woes continue.
Treatment table
City seemingly paid the price for rushing back Germano as a solution for Iain Ramsay's failure to adapt to the position in the first three rounds of the campaign. If it was indeed a gamble, it backfired, the Argentine forced off with what appeared to be a hamstring issues inside the first 30 minutes.
Back to the drawing board
Whoever fills out the Adelaide United team sheet needs to have their pen licence checked. The formation was listed as 3-4-3, with Craig Goodwin at outside left and Sergio Cirio in a central attacking midfield role.
When the match started it was apparent the Reds were playing the same 4-3-3 they have used since Round 2, with Goodwin at left fullback and Cirio in his usual spot at outside left.
The press weren't fooled and Van 't Schip was unlikely to have been either, so perhaps teams should dispense with the feeble attempt at mind games and back themselves to win without resorting to deception.
The Final Word
The Reds did it tough at AAMI Park, proving they can grind out a result as well as blow teams away and only adding further to their early championship credentials ahead of a big game at home to Sydney FC next weekend.
City haven't been able to win with World Cup and Champions League winner Villa in their ranks. How will they get off the mark when the former Barcelona and Atletico Madrid man leaves for New York next week? Fellow strugglers Brisbane Roar are their next opponents, and the champions may well fancy their chances against their winless visitors.
When will refs take a minute to check Twitter and get the consensus on card colour? #MCYvADL
— JAL (@jalmelb) October 31, 2014
Teams
Melbourne City: Redmayne, Germano (Garrucio 27'), Kisnorbo, Wielaert, Hoffman, Paartalu, Mooy, Murdocca, Villa, Dugandzic (Williams 58'), Duff.
Adelaide City: Galekovic, Elrich, Boogard, Malik, Isaias, Cirio, Carrusca, Jeggo, Goodwin, Djite (McGowan 84'), Mabil (Kamau 71').
Scorers: Kisnorbo (9'), Djite (39'), Carrusca, penalty (80')
Red cards: None
Yellow cards: Hoffman (53'), Kisnorbo 63')
Conditions: 29°C, dry
Attendance: 13,083@AAMI Park