Copa Sudamericana: Grêmio takes slender lead against Colombians
Marco Antonio headed home a Zé Roberto corner in the 36th minute to give Grêmio a goal advantage ahead of their trip to Colombia.
Grêmio could have had more but a strong performance by Millionarios keeper Luis Delgado kept the scoreline to a single goal.
The keeper was beaten once in the second half by an Andre Lima header but the effort was ruled out for offside.
Vanderlei Luxemburgo's side will face Millionarios in the second leg on November 15 as they compete for a place in the semi-finals.
Grêmio midfielder Marquinhos was satisfied with the performance: "The main goal was a victory, so a 1-0 score line is good. Now we'll go to Colombia to try to score more."
The winners of this tie will face Paraguay's Cerro Porteno or Argentina's Tigre.
São Paulo will be facing Chilean side Universidad de Chile in tonight's quarter-final as Brazil's other representative.