Dozier was leading off the inning with the Twins trailing, 6-5. After reaching second and third on consecutive groundouts, he scored the tying run on Kurt Suzuki's single.
Gardenhire's challenges have been overturned 13 times in 25 attempts. He was thrown out of the game on Tuesday against the Royals after questioning a ruling following a review.
In the ninth inning, White Sox manager Robin Ventura challenged Cedarstorm's call, when Dozier was ruled safe on a groundout that ricocheted off pitcher Jake Petricka.
The call was confirmed after a 50-second review. Dozier scored on a Suzuki fielder's choice three batters later, trimming the White Sox lead to 10-8, which became the final score.
Daniel Kramer is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.