Jumaa arrived as a late substitute for Subait Khater and grabbed the winner two minutes from time after being set up inside the box by Fernandinho, the Brazilian forward who wove his way through the defence before slipping the ball to the goalscorer.
Luiz Henrique, the Brazilian midfielder, had given the visitors to an early lead before Ali Al Ameri headed the equaliser from a dipping free kick by Khater midway through the second half at the Mohammed bin Zayed Stadium.
The result moved Jazira up to sixth in the league after their fourth victory of the season.
"I am very glad that I got the opportunity to get on to the pitch and score this all important goal," Jumaa said in a post-match television interview. "It was an excellent team effort and I was just fortunate to be at the right place in the right time. Thank God, it was just a great feeling we won."
Shabab took the lead when Ciel picked up a pass from Sami Anbar in the 12th minute and slipped it towards the unmarked Henrique and his left-footed shot beat Ali Kasheif, the Jazira keeper, and found the corner of the net.
Jazira pressed hard for the equaliser with Ali Mabkhout wide on a volley and later his low shot went straight at Salem Abdulla, the Shabab keeper.
Abdulla also did well to push out a free kick from Matias Delgado. Shabab stayed composed to weather the brief storm and gradually turned the tide.
They could have doubled their lead on the half-hour. Ciel set up Essa Obaid six yards in front of the goal but his weak effort was smothered by Kasheif and a second effort went wide.
Obaid picked up an injury and was replaced by Edgar Bruno, the Brazilian forward, two minutes before the break.
Jazira began the second half with more resolve and intensity but the Shabab defence stood firm and they were dangerous on the counterattack.
A Bruno effort took a lucky deflection off Abdulla Mousa inside the box and Ciel's low shot from 25 yards was well held by Kasheif.
Jazira were missing the suspended Ricardo Oliveira, the former AC Milan forward, and their attack did not pack the same power without him. Yet they still showed real character to win.
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