The Tigers (74-87) entered this season the four-time defending division champion but were hurt by significant injuries and shaky pitching in falling to last place for the first time in seven years.
Chicago finished the season at 76-86, in fourth in the Central, a slight improvement over last year, when the Sox won 73 games.
Norris (3-2) didn’t give up a hit until Trayce Thompson’s triple in the fourth. Thompson was stranded on third, however, when Alexei Ramirez hit into an inning-ending double play.