The Brazilian marksman rose above the Dhafra defence to head in a Subait Khater freekick with 27 minutes played to give a depleted Jazira all three points.
The wins takes Jazira's tally to seven points, two behind Group B leaders Al Wasl, with four games left to play.
Jazira are well placed in all three domestic competitions at the halfway stage. They are second in the Pro League, qualified for the last eight of the President's Cup and now are in contention to reach the knockout stages of the Etisalat Cup.
Jazira coach Paulo Bonamigo was without five of his Emirati contingent, who are away on national team duty as the UAE prepare for next week's Gulf Cup in Bahrain, while influential midfielders Ibrahim Diaky and Matias Delgado were left out as a precaution as they are still recovering from injuries.
"At this point when most of the players are on national duty and when some players are recovering from injuries it is the three points that matter," the Jazira coach, said.
"We created several chances but unfortunately couldn't convert them to goals. But this is not unusual when we have a different combination. We can still take the result as a positive."
Laurent Banide, the Dhafra coach, fielded a largely second-string side, who gave a good account of themselves despite rarely threatening and going large periods without possession.
"We need to provide all the players an opportunity to play and tonight they showed they can compete against any opposition," Banide, the Frenchman, said.
"We fielded the fringe players because we can't have the same players to play in both, the league and the Etisalat Cup. But we came here to win. And we gave Jazira a good fight. I am very satisfied with my players."
Jazira were definitely the better team on the night as they enjoyed possession and territorial advantage for much of the 90 minutes.
The former AC Milan and Real Betis striker Oliveira always looked the most likely to score and was unlucky not to open his account on 12 minutes when his free kick from just outside the box crashed against the corner of the crossbar.
Fellow Brazilian Fernandinho sent an effort wide when through on goal four minutes later as his goal-drought extended to 18 games in Jazira colours.
He blasted one effort from inside the box high, wide and not very handsome, while the second-half substitute Ahmed Juma should also have added to the score but his lobbed effort also sailed over.
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