Ibrahim Diaky opened the scoring in the 15th minute and the Brazilian pair, Bare and Ricardo Oliveira, combined to strike three times in the second half for the Pro League champions to avenge a 3-1 home defeat in a league game last month at the Mohammed bin Zayed Stadium.
For the opener, Bare collected a cross from Oliveira and played it back to Diaky, just outside the box, and the midfielder sent a low shot past the Al Ain goalkeeper Walid Salem.
Jazira were left one player short after 30 minutes when Abdulraheem Jumaa was sent off for an ugly tackle on Ahmed Al Shamsi.
Looking to capitalise on their numerical advantage, the visitors came close to levelling when Al Shamsi's free kick hit the glove of Khalid Saif Al Sinani, the Jazira goalkeeper, and came off the post before being cleared by Lucas Neill, the Australian defender.
They also wasted a few chances due to poor finishing, with both Yasser Al Qahtani and Al Shamsi twice off target from close range.
Mohammed Malallah's effort then crashed against the crossbar as the home side held on to their one-goal lead at the break.
Bare doubled the lead with a close-range shot after Oliveira back-heeled the ball towards him.
The the architect of that goal added the third from a penalty awarded for a handball against the Al Ain defender Mohammed Ayub.
Bare completed the rout with a neat chip in added time.
The result took Jazira's tally to 16 and six clear of Al Ain with three games left. Al Wasl and Dubai, both on nine points each, will battle it out tonight to keep their own hopes alive to reach the knockout stage of the competition.
It was one of the worst defeats for Al Ain, who were unbeaten in the league until last weekend's 2-0 defeat to Al Nasr.
A silver lining for Al Ain in the game was the return of Omar Abdulrahman, their playmaker, for the first time in the season after a knee surgery. He came in on the hour but was unable to energise a side depleted by injuries and international commitments.
In a Group A match on Friday night, Al Wahda beat Emirates 2-0 to advance to the semi-finals. In Group B, Ajman held Nasr 1-1.
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