Masterson (10-6) dominated Chicago, scattering six hits and issuing just one walk as the Indians completed their first four-game series sweep of the White Sox since 1948, the year of the Tribe's last World Series title.
The right-hander struck out eight while placing 73 of his 112 pitches for strikes.
Yan Gomes supplied three hits for the Indians.
Chisox starter Chris Sale (5-7) was tagged with the loss, surrendering three runs on seven hits over eight frames. He struck out 10.
Reeling Chicago fell for the 23rd time in 31 games.
Toddler uninjured after being knocked over by Obama family dog
Man spent 15 hours in jail for plugging electric car into an outlet at a school