The rookie right-hander stayed in just long enough to become the first Rangers starter to get a victory in June.
David Murphy and Leonys Martin singled and scored in Texas' two-run fifth, and the Rangers rallied to beat the A's 9-4 on Wednesday night.
"For sure, this win goes to our offense, they came back and helped me out, picked me up," said Grimm, the Bristol, Va., native who leads American League rookies with six wins.
Oakland went ahead 3-2 in the fifth on a three-run homer by Chris Young, which came after Grimm walked two batters.
Ian Kinsler hit a sacrifice fly off Tommy Milone (6-7) in the bottom half that scored Murphy. Martin raced home on a grounder for the go-ahead run.
"I think we can go out there now and be competitive," Rangers manager Ron Washington said. "I think we got the monkey off our back as far as having a total drought offensively. I think some guys are starting do some things all throughout the lineup. ... We start getting more consistent, then we'll get back to playing our baseball."
Nelson Cruz, hitting third for the first time this season in Washington's 50th different batting order in 72 games, had three hits and drove in two runs. Lance Berkman homered.
Rangers starting pitchers had gone 17 consecutive games without a win since Derek Holland beat Kansas City on May 31. The team's previous longest such stretch was 16 in a row in 1975.
They scored nine runs for the first time since a 9-5 win over Arizona on May 30. Their 14 hits were the most since the game Holland won.
Texas opened the four-game series with an 8-7 win Monday night. That snapped a six-game losing streak when the Rangers scored a combined eight runs.
With only their fourth win in 14 games, the Rangers pulled within two games of Oakland. The A's will go for a split in the finale of the four-game series Thursday, but will leave Texas still in first place regardless of what happens.
In the Oakland fifth, Grimm (6-5) walked Josh Reddick, a .206 hitter, before a wild pitch and then a walk to No. 9 hitter Eric Sogard. Young homered onto the hill in straightaway center field for a 3-2 lead.
Before that, the A's didn't have a runner get past first base. But their lead didn't last long after Grimm's last pitch.
Grimm allowed three hits, struck out three and walked three.
"He got us five and kept us in the game. That's all we ask," Washington said. "We were able to do the rest for him."