Frank Fabra opened the scoring at the Bombonera Stadium in Buenos Aires on Wednesday before two goals in as many minutes from Mateo Casierra saw the Colombian side claim the lead, reports Xinhua.
Tevez equalised just before halftime and then Andres Chavez put the hosts in front just after the interval. Deportivo were reduced to 10 men when German Mera was shown a second yellow card in the 70th minute.
Boca capitalized on the numerical advantage with Tevez, Leonardo Jara and Sebastian Palacios all finding the net in the last 20 minutes.
The result saw Boca end the group stage as Group 3 leaders with 12 points from six matches, three points ahead of second-placed Racing Club, who also progressed to the knockout phase after a 1-1 draw over Bolivar in La Paz.
In other matches on Wednesday, Cerro Porteno secured their passage to the next phase with a 1-0 win over Independiente Santa Fe while Corinthians romped to a 6-0 victory over Cobresal.