Austin Meadows had a single, double, home run and three RBIs, while Glasnow struck out a career-high 11 in six innings in a 9-1 win over the White Sox on Wednesday that completed the Rays' first series sweep in Chicago.
Tommy Pham homered twice and extended his on-base streak to a club record 45 games, as the AL East-leading Rays won their fourth straight to improve to 10-3, their best start since 2010. They outscored Chicago 24-7 over three games.
Meadows was 7 for 10 in the series with two homers, seven RBIs and four runs.
Reynaldo Lopez (0-2) fell behind 3-0 within 18 pitches.
Jalen Beeks gave up one run in three innings for his first professional save, allowing Yonder Alonso's run-scoring groundout in the ninth.
Chicago entered with a major league-worst 6.72 ERA, and Lopez allowed eight runs, 10 hits, and four walks in 4 1/3 innings. He has failed to get past the fifth inning in all three starts.
Meadows led off the game with a single, and Pham sent the next pitch into the right-center field bleachers. Brandon Lowe doubled with one out, and Avisail Garcia hit the first of two RBI singles.
Meadows and Pham hit back-to-back homers for a 5-0 lead in the fourth. Pham's opposite-field drive to right-center was his eighth multi-homer game.