"That's one of our worst defensive games in a long time," Angels manager Mike Scioscia said.
Taking their fifth consecutive series from the Angels, the Rangers moved to within 3 1/2 games of the American League West lead.
"This means a lot," Rangers right fielder Josh Hamiton said. "We're getting to the time of the season where every game means a little bit more, especially against the guys leading the division.
"It would be nice to play the same against other teams as we do the Angels, keep that same fire and intensity."
Lackey fell to 8-4 with his first loss in six starts, dating to a July 7 setback against the Rangers at home.
A dropped fly ball by reliable Bobby Abreu in right field cost Lackey the first two runs in the fourth inning, and soon the only positive energy was found in the visitors' dugout.
"I closed my glove too early," Abreu said, unable to recall it ever happening before to him. "It was bad. I should make that play. No excuses. That cost part of the game. Lackey could be out of the inning. My fault."
The Angels' offense, overly selective in the judgment of Scioscia, never generated any juice. Leadoff catalyst Chone Figgins ended a streak of 92 consecutive starts, giving way to Maicer Izturis at third base and atop the batting order.
Izturis' line-drive single to center with two outs in the sixth inning ended Holland's no-hit bid. Vladimir Guerrero and Jeff Mathis singled in the seventh and eighth, respectively, but none of the Angels' runners advanced farther than first.
Two of the four runs allowed by Lackey across 6 2/3 innings were unearned. Scioscia summoned Darren Oliver to retire Hamilton to close the seventh after Marlon Byrd's sacrifice fly had delivered David Murphy.
Rangers catcher Taylor Teagarden blasted a two-run homer in the eighth and Byrd hit a solo shot in the ninth.
Lackey finished with eight strikeouts while yielding eight hits and two walks.
"That's the best stuff I've thrown all year," Lackey said. "The game's about wins and losses. The rest of it is ... whatever."
The Rangers scored twice in the fourth on Abreu's error, off the bat of recent callup Esteban German.
Hank Blalock had beaten out an infield hit right before German's fly ball. Lackey and first baseman Robb Quinlan met near the bag, unsure who was taking Howard Kendrick's toss as the second baseman hesitated, waiting for a receiver.
"He kinda went after the ball," Lackey said of Quinlan. "I saw him come back toward the bag. He saw me and assumed I was going to have it."
The Rangers added a run in the fifth when Byrd singled home Elvis Andrus after two hits and a catcher's interference error on Mathis had loaded the bases. Juan Rivera's strong throw from left cut down Michael Young at the plate.
Lackey was visibly distressed at times, but after the game he had cooled down.
"It just happens every now and again," he said. "We've played pretty good defense all year. We'll come out tomorrow and get after it."
Mathis came to the mound several times to try to calm down his pitcher.
"Everybody knows he's passionate in what he does," Mathis said. "That's John. He's intense. He's going to get frustrated, going to get hyped up. That's the way he plays the game. He doesn't like giving up runs. That's him."
Mathis lauded both starters.
"John had good stuff and was locating well," Mathis said, adding that Holland "has got good stuff and was locating his fastball, getting early [count] outs. He had us off balance all day."
Scioscia traced that to a "passive" offensive approach that had the Angels tilting at windmills against Holland, wise beyond his years.
"He came at us," Scioscia said. "It wasn't any secret. He threw a lot of first-pitch fastballs and did as good a job of getting two-pitch outs as we've seen in a long time. He was ahead in the count all day long. That's partially due to us trying to work pitches early, and he was coming right after us.
"He pitched a terrific game."
Holland moved to 5-7 with a dominant performance, showing why the Rangers were so reluctant to include him in Roy Halladay trade talks with Toronto. His stretch of 5 2/3 hitless innings was the longest by a Rangers pitcher since Juan Dominguez lasted six innings without yielding a hit against the Royals on Sept. 3, 2005.
Texas is 24-13 against the AL West, while the Angels are 15-19 inside the division.
The teams have two series left, three games in Texas on Sept. 18-20 and four in Anaheim the final week of the season, Sept. 28-Oct. 1.
"They can beat us 18 times," Lackey said, "and if we play 19 games better against everybody else, it doesn't matter."