Oliver, who pitched for the Angels from 2007-09, and Guerrero, an offensive mainstay in Anaheim from 2004-09, both signed with Texas as free agents in the offseason.
Oliver had to be careful not to smile when facing longtime friends.
"It's hard to look those guys in the face when I'm out there pitching," Oliver said. "I might start laughing or something because I know them so good.
"They know me pretty good and I know them pretty good. It's fun. That's why we're out here playing. I'm sure they couldn't wait to face me and I couldn't wait to face them. After three years, you get to know guys pretty well."
Oliver has allowed one earned run over his last 12 appearances to lower his ERA from 3.86 to 1.74.
"Darren Oliver gave us two innings of excellent baseball," Rangers manager Ron Washington said. "He saved us there."
Guerrero has also been a major contributor to the Rangers' surge into first place in the division, leading the team with 31 RBIs.
He insisted earlier Monday that he has no desire to show the Angels that they erred by not re-signing him.
"I don't need to show anything to anybody," Guerrero said through a translator. "I always feel I've done my job my whole career."
Holland (2-0) allowed three runs and five hits in 5 1/3 innings in his second start since being recalled from Triple-A Oklahoma City on May 12.
Neftali Feliz got three outs for his ninth save in 11 chances as the Rangers opened a seven-game homestand after being swept in a three-game weekend series in Toronto.
Feliz, Oliver and Dustin Nippert retired the final 11 Angels.
Mike Napoli hit a deep drive with one out in the ninth in a bid for his second homer of the game, but Texas center fielder Julio Borbon made the catch with his back against the wall. The wind wasn't blowing as briskly as usual on Monday night, and Feliz was the beneficiary.
"Some balls were getting knocked down a little bit," Angels manager Mike Scioscia said. "I don't think the ball was flying like it has the potential to here, that's for sure."
Napoli and Torii Hunter homered for the Angels, whose three-game winning streak ended.
Los Angeles starter Scott Kazmir (2-4) gave up four runs and nine hits in seven innings, his longest outing of the season.
Kazmir entered with a 6-1 record and 2.05 ERA against Texas, his lowest ERA against any AL opponent.
Borbon led off Texas' four-run third by beating out an infield single, and he was awarded second when second baseman Howie Kendrick's throw to first bounced out of play for an error.
Ian Kinsler added an RBI double, and after Guerrero's bloop double, Cruz's two-run double made it 4-0.
Holland didn't allow a hit until the fifth when Juan Rivera had a one-out infield single, the first of four straight hits by the Angels.
Napoli followed with a two-run shot to narrow the deficit to 4-2, and Hunter led off the sixth with a 420-foot drive to pull the Angels within 4-3.
But the bottom line was another road loss for the Angels, who have dropped nine of 11 away from Anaheim.
"We need to go into a visiting ballpark and make that field yours, and we're not doing that this year," Scioscia said. "We're not doing the things we need to do on a consistent basis. Tonight we let some things get through the cracks and we've got to tighten some things up."
The first pitch was delayed 18 minutes while the field was readied after heavy pregame rain. ... Washington gave OF Josh Hamilton a night off, saying he is fatigued "both mentally and physically." Hamilton, 1 for 13 during the weekend series in Toronto, wanted to stay in the lineup, but admitted he was "clueless" at the plate against the Blue Jays. Hamilton started 36 of the Rangers' first 38 games this season. ... Angels RF Bobby Abreu was scratched from the starting lineup due to back stiffness. He was replaced by Reggie Willits. Abreu pinch hit in the ninth, striking out to end the game.