Andres Chavez bagged a brace and Jose Fuenzalida also scored as Boca accounted for 10-man Central in the return leg of their second-round tie at La Bombonera on Thursday.
Boca - two-time winners of the tournament after back-to-back triumphs in 2004-05 - advanced to the round of 16 with a 4-1 aggregate victory.
Next up for Boca is the winner of Deportivo Capiata and Caracas, with their tie locked at 1-1 after the first leg.
The Argentine giants have enjoyed life under coach Rodolfo Arruabarrena, who succeeded Carlos Bianchi in late August, unbeaten in three games prior to Thursday's fixture.
And that good form continued against Central as the home side hit the front thanks to Chavez in the 20th minute.
Jonathan Calleri chested the ball down for onrushing team-mate Chavez, who volleyed powerfully into the top-left corner of the net from the edge of the box.
Central's woes were compounded in the 36th minute, when Lucas Acevedo saw red for a second bookable offence.
Boca eventually made the most of their numerical advantage, with Chavez netting his second goal of the game after 71 minutes, sending a diving header past Central goalkeeper Mauricio Caranta.
Chile international Fuenzalida came off the bench and completed the scoring with six minutes remaining.
Meanwhile, Emelec defeated Uruguayan side River Plate 2-1 in the opening leg of their second-round meeting.
Goals from Marcos Mondaini and Miller Bolanos gave the Ecuadorian hosts a two-goal buffer after 48 minutes, while Michael Santos netted a late away goal from the penalty spot.
River will be without defender Claudio Herrera for the second leg in Uruguay following his dismissal 15 minutes from time.