Millwood (2-4), who had been sidelined since April 28 with a strained left hamstring, allowed four runs and three hits with three walks.
"I kind of misstepped, actually to the first batter in the game," Millwood said. "It got sorer as I went on. In the second inning, I couldn't get out over my front leg. It's not easy to pitch that way."
Jered Weaver (2-3) allowed six hits in a season-best seven innings for the Angels. He struck out five, walked two and threw 57 of 87 pitches for strikes.
"That's the best I've felt all year," Weaver said. "Everything was consistent. I feel like I'm back to normal. Getting a 4-0 lead in the first takes the pressure off the pitcher's shoulders."
The Angels took three of four from Texas in the series and have won six of seven against the Rangers this season.
The grand slam was the second of Kotchman's career. He has 11 home runs in three major league seasons, including three this year. He has two homers in three career at-bats against Millwood.
Kotchman, who walked in his other three plate appearances, attributed his success to working with hitting coach Mickey Hatcher.
"There was something in my setup with my feet that was affecting my balance," Kotchman said. "It's let me swing free and easy.
"The three walks, that's more my role on the team, to get on base. That's what's expected of me."
Reggie Willits and Gary Matthews Jr. walked and Orlando Cabrera singled to set up Kotchman's slam. Los Angeles has gone ahead in the first inning in each game against Texas, outscoring the Rangers 17-0.
"After the first inning, there's still eight more to play," Texas' Michael Young said. "We've got plenty of time to go out there and score runs."
After a 33-minute rain delay in the third, Los Angeles stretched its lead to 7-0 by scoring three times against Willie Eyre. Mike Napoli hit an RBI double and Tommy Murphy followed with a two-run single for the Angels.
Rangers manager Ron Washington was not optimistic about when Millwood would pitch again.
"Hamstrings are tough, and he uses his legs so much that we need his legs healthy," Washington said.
Kotchman was among a couple of Angels who had a strong series against the Rangers, making up for a rare off one by Vladimir Guerrero.
Guerrero has 21 homers and 51 RBI in 61 career games against the Rangers, but drove in just one run in the four-game series.
But Kotchman was 6-for-14 (.429) with five RBI, Willits stretched his hitting streak to nine games and was 6-for-17 (.353) with five runs scored, and Cabrera's two hits Monday put him at 8-for-20 (.400) with four runs and two RBI.
- Texas has been outscored in the first inning 31-8 this season, including 10-0 in this series.
- Rangers 1B Mark Teixeira's first-inning single stretched his hitting streak to 12 games.
- The Angels scored at least six runs in each of the four games against Texas.
- During the rain delay, Weaver went to the Angels' bullpen and threw 15 pitches. He said that helped him loosen up.