Coach Rodolfo Arruabarrena replaced Carlos Bianchi in late August, and Boca nabbed a crucial away goal under their new boss in their first leg with Rosario Central in his second match in charge, with the clash ending 1-1.
Also in Boca's favour ahead of Thursday's second leg is the unavailability of Rosario defender Alejandro Donatti, who saw red late on in their first match-up.
Boca's league derby with Racing Club was suspended on Sunday due to torrential rain, halting their progress as they led 1-0.
Boca's home domestic form has been sketchy, mixing two wins with two losses in their past four - while their most recent win in the Copa Sudamericana on home soil was four matches back in 2008.
River Plate will carry a 1-0 lead into their home second leg in another all-Argentina Primera Division clash with Godoy Cruz.
A 90th-minute goal from German Pezzella puts the tie on River's terms heading to their Buenos Aires home on Wednesday.
A third all-Argentine clash on Tuesday sees Estudiantes host Gimnasia La Plata in the second leg, after the first 90 minutes finished scoreless.
Ecuadorian outfit Barcelona take a 1-0 lead to Paraguay's Libertad for their second leg on Wednesday.
In first-leg matches, Ecuador's Independiente del Valle host Paraguayan club Cerro Porteno, while Venezuela's Caracas travel to Paraguay to tackle Deportivo Capiata.
Uruguay's Penarol welcome Colombian Primera A club Deportivo Cali, Chilean side Huachipato host Universidad Catolica of Ecuador, Bolivia's Club Universitario are at home to Peruvian outfit Cesar Vallejo and Uruguayan side River Plate are on the road at Ecuador's Emelec.