Medel scored from a Juan Roman Riquelme free-kick after 13 minutes and blasted home his second from outside the box four minutes into the second half of Argentine football's biggest derby.
Being sent off 15 minutes from time for a foul, his second bookable offence, appeared to merely heighten the esteem of the hard-core Boca fans who maintained a high tempo atmosphere of chanting throughout the match at the Bombonera.
"Gary shone today, he was really good," said Riquelme, who had a good match under the gaze of Argentina coach Diego Maradona, who was in his Boca box for the first time in a year.
"We believe we played well and deserved to win, we were clearly superior to River," Riquelme, who is out of Maradona's World Cup plans, told reporters.
Medel, a stocky, close-cropped 22-year-old ball winner who was signed from Universidad Catolica of Chile last July and could make a big impact at the World Cup, came back onto the field after the final whistle to celebrate with his team-mates.
It was the longest ever Superclasico. Only nine minutes were played before it was abandoned in torrential rain on Sunday with the score 0-0. Thursday's continuation lasted 81 minutes.
For Boca and River to both be struggling in the bottom half of the standings at the same time is a rarity and the fact they are not involved in the South American Libertadores Cup, a title they have won eight times between them, made it possible to re-schedule Thursday's game so quickly.
The atmosphere in the Bombonera compared with the best derbies between the two sides when they were fighting neck and neck for the league title. The chanting was constant, the sound deafening and the ticker tape abundant.
The match, however, was mediocre even if it was fought with passion, particularly from a Boca side determined to put behind them a run of seven games without winning.
Riquelme, with his intelligent playmaking and prompting of both goals, and Medel, with his commitment and scoring, were the outstanding performers.
Boca, after their second win in 10 matches, climbed to joint 14th with 11 points. River are a point ahead in 12th.
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