Nacional finished the quarter-final first leg tie in Sao Paulo with 10 men after substitute Roberto Brum was sent off in stoppage time for an off-the-ball incident.
Palmeiras, led by former Brazil and Real Madrid coach Vanderlei Luxemburgo and one of four Brazilian teams in the last eight, went ahead in the 55th minute when Diego Souza scored with a low shot from the edge of the area.
Nacional replied 10 minutes from time when substitute Santiago Garcia turned Oscar Morales' pass into the net from 12 metres, their only shot on target of the half.
Estudiantes, the only Argentine survivors, won 1-0 away to Defensor Sporting, another Uruguayan side, in the evening's other tie.
Defensor's Jorge Curbelo and Estudiantes defender Marcos Angeleri were sent off for fighting in the 24th minute.
"We did what we had to do," said Estudiantes captain Juan Sebastian Veron.
