Mitch Moreland hit a two-run homer and Grimm took a shutout into the sixth inning to help the Rangers snap their first three-game losing streak of the season with a 9-5 interleague victory against the Arizona Diamondbacks on Thursday.
Grimm (5-3) allowed four hits through five innings. The AL rookie leader in wins and strikeouts was replaced after Arizona's three-run sixth, and trails only ace Yu Darvish in victories on the Texas staff.
The 24-year-old Grimm, who made his debut last year, came up from the minors in April when opening-day starter Matt Harrison went on the disabled list with back trouble.
He figured to stick around awhile with Harrison out until at least August, and was the AL rookie of the month for April. Grimm gave up eight hits and two earned runs with three strikeouts in his third straight May win after starting the month with all three of his losses.
"He's gotten better as far as confidence-wise, believing and knowing that he belongs here," catcher A.J. Pierzynski said. "It just a progression with young guys. He continues to get better. You can see it in his face. You can see it when he takes the mound in his mannerisms."
Grimm lost his shutout when he gave up four straight hits in the sixth, starting with a double from Paul Goldschmidt, who tied a career high with four hits. An error by Leonys Martin in center on a single by Miguel Montero led to an unearned run.
"It's just all about battling and competing against these guys," Grimm said. "Be aggressive with them, but not overly aggressive obviously."
Texas cooled off Arizona starter Brandon McCarthy (2-4) on the way to a 9-0 lead. McCarthy, who lost for the first time since April 26 in his shortest outing of the season, gave up nine hits and six runs in just 2 2-3 innings.