The White Sox went to the bullpen, bringing Bennett Sousa in for starter Luis Giolito.
And while the Tigers had started to put together some good swings in the fourth, they went quietly in the fifth as Akil Baddoo and Spencer Torkelson both flew out to right and Tucker Barnhart grounded out to shortstop.
It was the second straight inning the Tigers went down in order.
Tigers work out of jam as White Sox lead, 3-0
The day is over for starter Eduardo Rodriguez, who gave up four hits and three runs in four innings, striking out two and walking a pair.