Uruguayan forward Santiago Silva gave Boca the lead with a long-range shot against the run of play in the 21st minute and Lucas Viatri scored the second just after the hour in the neutral city of San Juan.
Valentin Viola pulled one back for Racing Club in the 68th minute of Wednesday's match in front of a 35,000 crowd.
The match had been due scheduled for June 23 to round off the 2011-12 season but, in a story typical of the confusion which surrounds Argentine domestic football, was delayed because of fixture congestion.
As a result, it was played one week after the start of the 2012-13 season.
Modelled on European domestic cup competitions such as Spain's Copa del Rey and England's FA Cup, it featured 186 teams from the top five tiers of Argentine football in a knockout format.
Boca were also champions in 1969 on the only other occasion the tournament was completed.
In 1970, the tournament was abandoned after the first leg of the final had been played and was never held again until the Argentine FA relaunched it last season.
Boca's win gave them a small consolation after they failed to win the Argentine Clausura championship last season and were beaten in the South American Libertadores Cup final by Brazil's Corinthians.
They started the new league season on Saturday with a 3-0 defeat to Quilmes.