The 27-year-old right-back tied the score 1-1 in the 14th minute with a right-foot shot from near the penalty spot off the rebound of a free kick.
Yedlin received a yellow card for a hand ball in Caykur Rizespor's penalty area in the 52nd when he slid to block Braian Samudio's headed shot, leading to Milan Skoda's penalty kick that gave the visitors a 3-2 lead.
Yedlin was given his second yellow in the 79th for shoving Konrad Michalak from behind while on a run just outside the penalty area.
Galatasaray acquired Yedlin on a transfer from Newcastle on Feb. 1. The team is second in the league, two points behind Besiktas, but has played two more games. Caykur Rizespor is in 12th place.