Midfielder Walter Erviti scored the winner in 75th minute after Dario Cvitanich, Diego Rivero and Juan Roman Riquelme all struck the woodwork for Argentina's most popular side.
Sunday's win took Boca top of the Apertura championship - the first of two championships in the season with the teams meeting each other once in each competition - by one point from Atletico Rafaela. Unbeaten Boca have 14 points from six games.
Promoted Rafaela, the previous leaders, were held 0-0 by Newell's Old Boys and are a point behind.
Banfield remained pointless after six matches following their 1-0 defeat to Arsenal, where Emilio Zelaya scored the only goal after seven minutes.
Former Mexico and Costa Rica coach La Volpe blamed his team's wayward finishing as they stayed rooted to the bottom.
"If there are no goals, there is no happiness," he told reporters.
Champions Velez Sarsfield lost 1-0 at to home to Union Santa Fe as Paulo Rosales scored an 86th minute winner. Velez are tenth after their third defeat in six games.
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