Universidad secure progression
Angelo Henriquez got the only goal of the game late in the first half at the Estadio Malvinas Argentinas in Mendoza.
It had been an even match until first-half injury time, when Eugenio Mena's shot deflected into Henriquez's path and he fired home.
Godoy Cruz went close to an equaliser in the 69th minute, but Ruben Ramirez saw his header strike the post.
Although Universidad are assured of their passage from Group 8, coach Jorge Sampaoli immediately promised they would be targeting victory in their final group match against Colombia's Nacional.
"We'll do our best to get the three points against Nacional," he said. "Tonight we played a great first half and we should have scored one more goal. If we hadn't won, the qualification would have been at risk."
Internacional and reigning champions Santos drew 1-1 in Porto Alegre.
Santos top Group 1 on 10 points, with Inter two behind in second.
In Barranquilla, Colombia, hosts Junior eased past Chile's Universidad Catolica 3-0.
Ivan Valez put Junior ahead in the last minute of the first half, but it took until five minutes before full-time for Luis Alfonso Paez to double the lead.
Vladimir Hernandez then added a gloss to the scoreline with a late strike, giving Junior faint hope of qualifying even as they remain at the foot of the Group 3 standings.
In Ecuador, Emelec saw off Brazilian giants Flamengo 3-2 as Luciano Figueroa grabbed a brace.
Figueroa scored in either half but it needed a last-minute penalty from Fernando Gaibor to secure a win that puts Emelec third in Group Two.
Flamengo had led at the break after goals from Leo Moura and Deivid, and they remain in the hunt for the last 16 despite sinking to the foot of the standings.