Myers grounded to shortstop with a runner on third and two outs in the sixth. He appeared to beat the throw, but first-base umpire Cory Blaser called him out.
Rays manager Joe Maddon quickly made his way onto the field to challenge the call. The umpiring crew, headed by Jim Joyce, retreated to the third-base side to review the call.
After two minutes and 31 seconds passed, the call on the field was overturned, and Brandon Guyer, who doubled for the Rays' first hit of the game earlier in the inning, scored to cut the Rays' deficit against the White Sox to 10-2.
The Rays' second challenge came in the ninth with the Rays trailing 10-3. Sean Rodriguez grounded to third base and was called out at first. First baseman Andy Wilkins had to leap to bring down third baseman Marcus Semien's throw and Maddon felt as though he did not land on the bag before Rodriguez arrived.
But the call on the field was confirmed after a one-minute and 38-second review.
The Rays have had 48 challenges this season. Twenty-one of the challenges have been overturned, 13 have stood and 14 have been confirmed.