Wanderers SC began the match well, their midfield effective in breaking up Auckland's possession rhythm with midfielders Andre de Jong, Clayton Lewis and Moses Dyer leading the home side's charge without being able to regularly find a penetrating pass.
It was Auckland City who carved out the first quality scoring chance in the 28th minute, Fabrizio Tavano playing a delightful ball into the path of Tim Payne but the All Whites midfielder couldn't get the required contact under pressure in the area.
Just after the half hour mark, Wanderers came close to opening the scoring after a lovely exchange down the left saw Lewis freed to deliver into the six yard box where Auckland City goalkeeper Tamati Williams got the ball just ahead of De Jong to turn behind for a corner.
Two minutes later Auckland City enjoyed their best opportunity of the half as Ryan De Vries came marauding into the area but Wanderers' stopper Damian Hirst did superbly to save with his feet with the follow up shot by Sani Issa blocked by the retreating Wanderers defense.
Just before the break Wanderers crafted another good chance; after a Lewis corner was partially cleared, a cross returned to the back post was met firmly by Sam Brotherton but rather than nestling in the net, the ball skimmed off the top of the cross bar.
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After the restart, substitute David Browne provided some energy for Auckland City and he was thwarted by a last ditch tackle after dancing into the area before Tim Payne had a well-struck free kick superbly saved by Hirst low to his left.
Soon after it was All Whites legend Vicelich who hauled his side ahead with a powerful header from the set piece and although Wanderers kept trying - substitute Angus Kilkolly volleyed over after a wonderfully struck early cross from Lewis later in the half - it would be Vicelich's moment of quality which decided the outcome.
Tribulietx said his side still have work to do to recover their top domestic form after their ASB Premiership return. "I think we've got to get fresher. We need to recover our fitness, we need to recover our motivation as well to lift up our spirits to have a chance in the competition."
"We're going to get the rhythm back with these games and it's just a matter of getting our energy levels back up again and our touch and the understanding of the chemistry among the squad back again."
Meanwhile, Wanderers coach Darren Bazeley reflected on a game which he felt could have produced more than it did for his side.
"I'm disappointed to lose the game if I'm honest," Bazeley said, "We were very brave, we competed very well and we forced Auckland into giving away possession in their own half a lot of times. "[We] created some good chances and didn't take them and the game was decided on a set piece, on a corner. Big Ivan is good at that and he gets on the end of things and it's a good header."
"I thought overall we were well worth points today, we put a lot of hard work into it. The shape was good and we pressed them high and we didn't let them have any time on the ball.
"I don't think they played their normal game, we forced them into going long, we just weren't quite good enough to get that goal and put pressure on them."
Auckland City's next outing is Sunday's trip to Hawke's Bay United while Wanderers host Waitakere United at QBE Stadium on Saturday.