Glasnow (6-1) earned the win over Atlanta on Saturday, allowing two runs on five hits and one walk over seven innings while striking out 10.
Glasnow was removed from his start Saturday against the Blue Jays due to cramping in his right hand, Kirsten Watson of Spectrum SportsNet LA reports.
Glasnow (4-1) got the win over the Mets on Sunday, scattering seven hits across eight scoreless innings while striking out 10.
Glasnow (2-0) earned the win over San Francisco on Wednesday, allowing three runs on four hits and two walks while striking out seven batters over six innings.
Glasnow (1-0) earned the win Thursday against St. Louis. He allowed one run on two hits and a walk over six innings while striking out five.
Dodgers manager Dave Roberts said Sunday that Glasnow will start the team's home opener Thursday against St. Louis, David Vassegh of AM 570 LA Sports reports.
Glasnow tossed five innings, allowing two runs on two hits and four walks while striking out three batters in a no-decision against the Padres in South Korea on Wednesday.
Glasnow tossed 5.1 scoreless and hitless innings in a Cactus League contest against San Francisco on Tuesday. He struck out eight batters and allowed one walk.
Glasnow will start the Dodgers' Opening Day game March 20 in Seoul, South Korea versus the Padres.
The Dodgers signed Glasnow to a four-year, $110 million contract extension Friday, Ken Rosenthal of The Athletic reports.