Any draw in the second leg on November 15 will give Vanderlei Luxemburgo's Gremio a place in the penultimate stages of the South American club championship.
Marco Antonio scored the winning goal in the 36th minute, heading home a Ze Roberto corner which had been deflected into his path by Gilberto Silva.
Millonarios goalkeeper Luis Delgado had a strong second half, making several good saves to keep his team in the tie.
He was beaten in the final minute by Andre Lima's header from a Ze Roberto free-kick - but the effort was ruled out for offside.
Midfielder Marquinhos said afterwards: "The main goal was a victory, so a 1-0 scoreline is good. Now we'll go to Colombia to try to score more."
The winners of this tie will meet Paraguayan giants Cerro Porteno or Argentina's Tigre.
The other quarter-final ties will see reigning champions Universidad de Chile clash with Brazilian giants Sao Paulo, while 2010 champions Independiente of Argentina meet Chile's Universidad Catolica.