Right fielder Adolis García kept the Texas Rangers ahead, making a leaping catch near the wall in right-center for the final out of the inning.
Five Rangers pitchers limited the Sox to just three hits — a Luis Robert single in the first, a Yasmani Grandal home run in the sixth and a Romy González single in the seventh.
“We hit the ball a few times hard,” said Cairo, who subbed while Tony La Russa served a one-game suspension tied to Mike Wright Jr. throwing at Los Angeles Angels designated hitter Shohei Ohtani on Thursday.