The Croatian was on target with an expert volley from 25 yards out after Wahda enjoyed a neat passage of play in their opponent's half.
Marcelo Oliveira headed the equaliser after Al Hassan Keita had put the visitors ahead early in the first half.
Keita, the Guinea forward, picked up a long throw-in from Waleed Khaled and entered the penalty area before unleashing a bullet shot into the roof of the net to liven up the game on 48 minutes after a drab first half.
Branko Ivankovic, the Wahda coach, was not impressed by his team's performance at the Al Nahyan Stadium.
"Sometimes such performances are expected but this was far below than what was expected," he said. "The only silver lining was that we came from a goal down to win the game.
"This is not what we expected, especially with some very important league matches coming up from next week."
Wahda face Al Nasr in Dubai on Sunday, and the following week they play host to Al Ahli.
Dubai did not field most of their first team, including the strikers Richard Porta and Michael N'dri.
Rene Marsiglia, the coach, refused to confirm they have given up hopes for the Etisalat Cup.
"I expect all players in the squad to perform at the same high level when they are provided with the opportunity and I think they did play well," he said. "Wahda scored two excellent goals and won. We have 26 matches in the league. We need to rest some of the players and also provide others with playing chances and the Etisalat Cup is where we can experiment."
It could have been more trouble for Wahda had Mohammed Ibrahim been on target when one-on-one against Adel Al Hosani, the Wahda goalkeeper, when he was beautifully set up by Keita.
It proved costly for Dubai as Oliveira struck the equaliser in the very next attack. The Brazilian headed in a ball sent his way by Papa Waigo.
Wahda had a chance to take the lead when Oliveira was felled by Mohammed Jamal, the Dubai defender, in the penatly area but the Brazilian's meek spot kick was saved by Ahmed Salem.
Dubai were unlucky when Keita's effort from a counterattack ricocheted off the bar five minutes from time.