Reinaldo Rueda's men came from behind to beat Luis Suarez's side on Friday night as they recovered from their opening game defeat to give themselves a chance of progressing
Enner Valencia's brace led Ecuador to a 2-1 win over Honduras to keep their World Cup chances alive on Friday.
Valencia continued his fine form for his country as he scored for the sixth straight international game to see Reinaldo Rueda's men to an important win in Group E.
Carlo Costly had put Honduras ahead before Valencia's equaliser in the first half and his second in the 65th minute proved to be the winner at the Arena de Baixada in Curitiba.
Ecuador climb into second in Group E, behind a France team they face on Wednesday, while Honduras are still alive despite being bottom without a point.
Honduras coach Luis Fernando Suarez made two changes to the team that was well-beaten by France.
Jorge Claros replaced the suspended Wilson Palacios in midfield, while Andy Najar made way for Oscar Boniek Garcia out wide.
Ecuador, who suffered a late loss to Switzerland in their opening game, saw just one change to their starting XI as Oswaldo Minda took Carlos Armando Gruezo Arboleda's place in midfield.
Valencia had the first real chance in the 20th minute.
Frickson Erazo's long pass put Valencia through the centre of the Honduras defence, but the Pachuca forward missed the target in a one-on-one with Noel Valladares.
Ecuador looked most dangerous on the counter-attack, while Suarez's men had a good chance in the 27th minute.
A Garcia corner found Victor Bernardez, but the centre-back could only direct his free header well wide.
The game came to life just after the half-hour mark.
A long pass from Brayan Beckeles found Costly and, after Jorge Guagua failed to clear, the Real Espana forward fired a powerful left-footed strike past Alexander Dominguez in the 31st minute.
It ended a run of 510 minutes without scoring in World Cup matches for Honduras, dating back to the 1982 tournament.
But just three minutes later and Ecuador were level.
Valencia was quickest to react to Juan Carlos Paredes' deflected shot from the right to tap in the equaliser at the back post.
There was late drama in the half as Costly headed a Beckeles pass onto the post and Jerry Bengtson scrambled in the rebound.
Referee Ben Williams correctly ruled the goal out for a handball – while Bengtson also appeared to be offside – in a dramatic finish to the first half.
Dominguez kept out Beckeles' 20-yard effort early in the second half, while Ecuador were unlucky not to be awarded a penalty in the 58th minute when Felipe Caicedo appeared to be brought down.
Bengtson forced Dominguez into a save down low to his left moments later before Valencia put Rueda's side ahead in the 65th minute.
The 24-year-old climbed highest to nod in Walter Ayovi's fizzing set-piece from the left and the South Americans held on late in the encounter for a key win.