Argentina international forward Cristian Pavon put the hosts ahead at the Bombonera Stadium on Sunday by slotting home from a tight angle after a perfectly weighted Ramon Abila pass.
Former Manchester United, Manchester City and Juventus forward Carlos Tevez then drew a penalty after he was brought down by Gaston Gimenez.
Colombian midfielder Edwin Cardona scored his first goal of the season as he sent goalkeeper Alexander Dominguez the wrong way with the resultant spot-kick.
Sebastian Villa, introduced as a 77th-minute substitute for Tevez, netted the winner by latching onto Dario Benedetto’s through ball following another counter-attack and firing into the top corner.
Boca are three points behind leaders Racing Club with two wins and a draw from their four matches while Velez are 19th, six points off the pace.
In other matches on Sunday, Racing won 2-0 at home to Rosario Central, Independiente drew 2-2 at Estudiantes, Tigre won 2-0 at Aldosivi and Union Santa Fe drew 0-0 at Colon. IANS