Oliveira picked 10 different players in the starting XI for Cruzeiro's trip to Tupi in the Campeonato Mineiro compared to his line-up that faced Club Universitario in the Copa Libertadores opener.
Cruzeiro still won 3-0 against Tupi to remain top of their state championship standings, with only Willian Farias backing up from the scoreless draw in Bolivia last week.
On Tuesday, Cruzeiro will welcome Argentina's Huracan to Belo Horizonte and Oliveira claimed home support will be critical to the chances of his team - the two-time defending Brazilian champions.
"Cruzeiro is already used to infectious and unconditional support and in the Libertadores this will be crucial, and I'm sure we will pay it back in the field," Oliveira told Cruzeiro's website after the win over Tupi.
The likes of Leandro Damiao, Henrique, Marquinhos and Willian will be expected to return against Universitario.
After both opening round matches in Group Three ended in draws, Cruzeiro sit bottom of the table but could surge into the lead with a win against Huracan, who were held 2-2 at home by Mineros de Guayana.
Mineros will host Universitario in Venezuela on Tuesday.
In Group Seven, Libertad will meet Barcelona in Ecuador hoping to hand their hosts a second consecutive defeat, while leaders Estudiantes face a trip to Colombia's Atletico Nacional on Thursday.
Last year's Copa Sudamericana champions River Plate host Tigres UANL, while in other fixtures, Juan Aurich take on San Jose and San Lorenzo face Corinthians.
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