Grimm pitched seven shutout innings to win his second consecutive start and the Rangers beat the Minnesota Twins 4-3 on Friday night for their seventh victory in eight games.
Filling in for injured starter Matt Harrison, the 24-year-old Grimm allowed five hits, struck out four and walked none. The right-hander pitched six innings of two-run ball in an 11-3 victory over Seattle on Sunday.
Grimm's solid outing against Minnesota came one night after fellow rookie Nick Tepesch held the Twins to just one run.
"They have certainly been guys in our organization we've had a spotlight on, and because of the injuries opportunity presented itself," manager Ron Washington said. "We expect them to step up because they can pitch. I'm not going to sit here and say we knew exactly what we were going to get, but we knew they weren't afraid."
Joe Ortiz started the ninth for Texas, but was pulled allowing a pair of hits and striking out Chris Parmelee. Joe Nathan struck out Trevor Plouffe before rookie Oswaldo Arcia hit a three-run homer to get the Twins within one.
Nathan then got Ryan Doumit to fly out to earn his eighth save.
Grimm (2-0) and Tepesch have been solid since Texas lost Colby Lewis to right elbow surgery and Harrison was sidelined by an inflamed nerve in his lower back. The two have combined to go 4-1 with a 2.11 ERA this season.
"They know they have the potential to get guys out and that's what they're doing," shortstop Elvis Andrus said. "We trust in every guy who comes here and pitches. Either here or minor leagues, our mentality is to be ready."
Minnesota's biggest threat against Grimm came in the first inning when Joe Mauer reached on a throwing error by second baseman Kinsler and Justin Morneau hit a two-out double to put runners on second and third. But Parmelee flied out to end the inning.
The Twins managed just four baserunners the next seven innings.
"(Grimm) did a really nice job and kept us off balance," Twins manager Ron Gardenhire said. "A couple times when we did get some men out there he made big pitches when he had to. Hopefully we'll heat up here as an offense. We've been a little inconsistent."
With Lewis not expected to return until the end of May, Grimm relishes outings like Friday as he aims to prevent a return trip to Triple-A Round Rock.
"I just want to pitch for this team, whether it's in the rotation or not," Grimm said. "I want to prove that I belong here. That's the whole idea."
Scott Diamond (1-2) gave up three runs and 12 hits in 6 1/3 innings as the Twins lost their third straight and were shut out for the second time this season.
Texas took an early lead on consecutive one-out doubles by Andrus and Berkman in the first inning. Berkman then scored on a two-out double from Cruz, who has driven in at least one run in six straight games and 13 total during that stretch.
With back-to-back victories against Minnesota, the Rangers will remain undefeated through eight series to start the season. Texas has won five series and split two. ... Mauer went hitless for the second straight game, just the second time he's done so in back-to-back games this season. He's just 2 for 17 (.118) in his past five games after going 24 for 61 to start the season. ... The Rangers will start left-hander Derek Holland (1-1) on Saturday. Pedro Hernandez (0-0) will go for the Twins.