Boca, who won the 30-team Argentine championship on Sunday, completed a league and cup double while furious Central claimed that three key decisions, including both goals, went against them.
Central thought they had taken the lead in the first half of Wednesday's game when Marco Ruben scored with a powerful header but the goal was ruled offside and their enraged coach Eduardo Coudet was sent off for dissent.
There was more trouble early in the second when Boca's Gino Peruzzi went down under a challenge from Paulo Ferrari.
Although the foul appeared to take place outside the area, referee Diego Ceballos pointed to the spot and Nicolas Lodeiro converted.
Central were again aggrieved when Andres Chavez grabbed the second on the counter attack for Boca from what appeared to be an offside position.
As soon as the final whistle went, Central players surrounded the referee and police intervened to protect the official.
Coudet also approached the referee, gesticulating furiously.
"It's tough when they get it wrong like that in a final because we worked hard all year to get here," said Coudet.
"It really hurts. We didn't lose the final, they took it away from us."
Boca forward Carlos Tevez, who has inspired his side to two titles since joining them from Juventus in June, had little sympathy.
"There is always controversy and there will always be an excuse but Boca were the right winners," he said. "There was a lot of talking during the week and I think we showed why we're the champions of everything."
(Writing by Brian Homewood; Editing by Tony Jimenez)
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