Uruguay beat Peru 1-0 and Ecuador lost 3-1 to Paraguay, meaning both teams have 25 points with one match to play. Peru are on 21 points in fifth place.
Peru, Colombia (20 points) and Chile (19) will now vie for fifth place and a playoff spot against a team from the Asian confederation.
Peru host Paraguay, Colombia travel to Venezuela and Chile are at home against Uruguay on Tuesday in the final round of games.
Uruguay earned the win over Peru thanks to Giorgian de Arrascaeta's goal three minutes before half time. Peru were adamant a late looping shot held by Uruguay keeper Sergio Rochet had crossed the line but the referee waved away their claims for an equaliser.
Peru's defeat meant Ecuador qualified regardless of their result in Paraguay and they were overrun by the home side, who gave coach Guillermo Barros Schelotto his first win since he took over in October last year.
Robert Morales put Paraguay ahead after 10 minutes and Piero Hincapie put through his own goal on the stroke of half time to give the hosts a 2-0 lead at the break.
Miguel Almiron made it 3-0 nine minutes into the second half before Jordy Caicedo scored for Ecuador with five minutes left. It was Paraguay's first win in eight games.
Also on Thursday, Brazil beat Chile 4-0 at the Maracana stadium, with the aid of two penalties from Neymar and Philippe Coutinho.