Junior, beaten for the first time after four wins, had already qualified and remain top of the group with 12 points, two more than Gremio, after five matches.
Gremio are the sixth team to have reached the last 16 before the end of the group phase. Paraguay's Libertad and former champions Cruzeiro of Brazil, Estudiantes of Argentina and Penarol of Uruguay have also qualified.
Tricky winger Lucio put Gremio ahead just past the half-hour mark with a low shot from the left and striker Borges increased their lead after an hour when he backheeled a cross into the net from close range.
Junior had defender Jaider Romero sent off in the 66th minute for a second booking.
Wilstermann of Bolivia picked up their first point after four defeats in Group Six with a 0-0 draw at home to Emelec.
A victory at altitude in Cochabamba would have put Emelec level with title holders Internacional of Brazil on 10 points at the top of the group. Instead Emelec remain third with eight, a point behind Chiapas of Mexico.
Inter are at home to Emelec in a decider in Porto Alegre in two weeks time while Chiapas visit Wilstermann in Cochabamba.
Argentina's Velez Sarsfield, champions in 1994, draw 0-0 away to Universidad Catolica of Chile and will need to win their final Group Four match at Venezuelan leaders Caracas FC next week to reach the last 16.
With one round of matches to go, Caracas have nine points, Catolica eight, Velez seven and Chile's Union Espanola four.
Velez midfielder Augusto Fernandez was sent off in the 65th minute for a second booking after making a dangerous challenge.
