Kweuke gave the away side an early lead on 20 minutes and Rizespor led until the third minute of additional time.
Rangelov equalised in the last minute of additional time to extend Konyaspor’s unbeaten home run to six games.
Konyaspor face Bursaspor in their final game of the season, the Anatolian Eagles will gain their highest points tally in club history with a win against the Green Crocodiles.
Torku Konyaspor 1 -1 Çaykur Rizespor
Stadium: Konya Büyükşehir Belediyesi Torku Arena
Referee: Deniz Ateş Bitnel, Süleyman Özay, Cemal Bingül
Torku Konyaspor: Kaya Tarakçı, Ali Turan, Mehmet Güven, Ömer Ali Şahiner, Ali Çamdalı (min. 83 Vedat Bora), Torje, Vukovic, Djalma (min. 70 Rangelov), Mehmet Uslu, Kenan Özer (min. 70 Recep Aydın), Hasan Kabze
Çaykur Rizespor: Serkan Kırıntılı, Eren Albayrak, Viera, Giray Kaçar, Orhan Ovacıklı, Koray Altınay, Sylvestre (min. 77 Oboabona), Kıvanç Karakaş (min. 60 Holosko), Deniz Kadah, Sercan Kaya, Kweuke (min. 85 Lafferty)
Goals: min. 20 Kweuke (Çaykur Rizespor), min. 90+3 Rangelov (Torku Konyaspor)
Yellow Cards: min. 38 Koray Altınay, min. 70 Viera (Çaykur Rizespor)