Quevedo's stunning late-season flurry has given them hope of sustaining their top-flight status for 2014, as their fourth win in five took them to 22 points in the second stage of the season.
Jose Mora's men remain in the drop zone, with points from both phases contributing to relegation, with Quevedo (45 points) in striking distance of LDU Loja (46), Deportivo Cuenca (46) and Manta (48) heading to the final match of 2013.
Quevedo, though, have the toughest of battles to keep their Primera A status, with a trip to champions Emelec on the final day on Sunday.
LDU Loja also won to stay above Quevedo in the relegation battle, as they beat Independiente del Valle 2-1 at home - arresting a deficit inside the game's final 20 minutes.
Loja will venture to Deportivo Quito on the final day, needing to win or relying on Quevedo or Cuenca to slip up.
Cuenca were dragged right back into the relegation dogfight after going down 2-1 at Quito.
Cuenca led when Andres Rios struck prior to the half-time interval, but Quito equalised before the whistle through Enrique Vera prior to Luis Santana's 80th-minute winner.
Manta failed to completely guarantee their top-flight status with a 0-0 draw at home to Emelec, but they are all but secure with point advantages on the other three sides in relegation contention.
Independiente del Valle host Manta next Sunday, with the visitors needing a point to sew up their Primera A place.
Wins to each of Loja, Cuenca and Quevedo combined with a Manta loss is the only scenario that would relegate the latter.
In other results, El Nacional beat the already relegated Macara 2-0, while Universidad Catolica had a 1-0 road win at Barcelona.
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