The Tigers lost for the eighth time in 11 games and failed in their bid to win two in a row for the first time since May 26.
Detroit overcame an early 4-0 deficit and took a one-run lead in the eighth on a solo homer by Delmon Young.
Cincinnati tied it in the bottom half of the inning when Todd Frazier doubled home Cairo.
Frazier did not start at third base for the Reds Friday due to back spasms and appeared in a pinch-hitting role. Cairo replaced Frazier at third base and wound up scoring both the tying and winning runs.
With Phil Coke (1-2) starting his second full inning of work, Cairo opened the 10th with a triple. He did not attempt to score when Ryan Hanigan grounded out to third, but he broke for the plate and scored when pinch-hitter Wilson Valdez hit a bouncing ball to first base.
Sam LeCure (2-1) got the win by working the ninth and 10th innings. He did not give up a hit and struck out three.