Central defender Andres Scotti headed the only goal from a corner midway through the first half to hand Boca their third defeat in four matches in all competitions and second at home in Libertadores Cup Group One.
The return of playmaker Juan Roman Riquelme, who shared in several titles with Bianchi in previous spells at the club, has not sparked Boca yet. They were the better side but lukewarm in attack.
"We had one loss of concentration and we couldn't score, but I think we played a good match... we deserved more," Boca's Uruguayan midfielder Ribair Rodriguez told Fox Sports.
Boca were beaten at home by Union in the league at the weekend in Riquelme's first match in eight months and he failed to inspire the six-times South American champions again on Thursday night.
Nacional lead the group with seven points, three ahead of Mexico's Toluca, who also won at Boca three weeks ago. Boca have three points from their 2-1 away win over Barcelona of Ecuador last week.
Three-times champions Nacional were down to 10 men from the 73rd minute after defender Alejandro Lembo was sent off for dissent so he will be missing when the teams meet again at the Centenario in Montevideo next week.
