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.