Striker Altan Aksoy notched what proved to be the winner as early as the eighth minute as Rizespor secured a precious win.
Konyaspor's Cedric Sabin was sent-off in the 21st minute before teammate Erman Ozgur followed him on the sidelines in the 71st minute.
Rizespor's Egyptian duo Beshir Al-Tabie and Ibrahim Saied didn't take part in the match due to suspension while their Konyaspor compatriots Abdul-Zaher Al-Saqqa and Mohamed Abdullah were included in the starting line-up.
The struggling club lie third from bottom with 39 points and will take on already-relegated Sakaryaspor in the last round of the Turkish League.
Konyaspor have lost any hopes of playing in the UEFA Cup next season as they remained in sixth place on 45 points.
Elsewhere, Ayman Abdul-Aziz's Trabzonspor secured their place in the UEFA Cup after defeating Bursaspor 3-1.
Abdul-Aziz played the full 90 minutes and put in a good display to help Trabzonspor move to fourth place on 52 points, four ahead of fifth-placed Kayserispor with one match to go.