Boca, who have conceded more goals than any other team in the Clausura championship at an average of two a game, were eclipsed by a Carlos Luna hat-trick.
"I'm not being taken out of here even (if I'm) dead," said defiant Boca coach Abel Alves, whose team have gone seven matches without a win and lost their last two.
"The match with River is for us to resurface. We can't go any lower," he told a news conference.
Luna struck his first in the 10th minute, headed his second just before half time and placed his third well clear of keeper Javier Garcia's dive 13 minutes from time.
Boca striker Lucas Viatri could have pulled one back in the final minutes but his two efforts in a single attack came back off the woodwork.
River notched their third win to give themselves the perfect boost for the visit to Boca's Bombonera (Chocolate box) cauldron next Sunday.
"There was a lot at stake. We had to win whatever way possible," said River Plate captain Marcelo Gallardo.
River struck inside two minutes when Huracan goalkeeper Gaston Monzon fumbled a shot and in the ensuing goalmouth melee the ball went in off defender Ezequiel Filipetto.
Midfielder Gustavo Canales scored the second in the 76th minute when he stole in behind a defender to head home left back Juan Manuel Diaz's shoulder high cross to the near post.
Independiente, the only member of Argentina's "Big Five" clubs in the top half of the 20-team standings, are top with 20 points after nine matches.
River are 11th with 12 points, Racing Club and San Lorenzo are 14th and 15th with 10 apiece and Boca 17th with eight.
Diego Simeone's San Lorenzo lost 1-0 at Rosario Central while Racing, with Roberto Ayala back in defence, were beaten 1-0 at home by Argentinos Juniors after their captain Claudio Yacob had a last-minute penalty saved.
