The Angels scored the go-ahead run in the sixth, courtesy of an infield single off reliever Ronald Belisario.
Belisario relieved starter Ted Lilly with two out and runners on the corners, the game tied at 2. Belisario was unable to handle a comebacker by Chris Nelson, and by the time Mark Ellis scooped it up, the second baseman had no play and Howie Kendrick had scored to put the Angels ahead, 3-2.
"If the ball doesn't hit Beli, we probably catch it," Dodgers manager Don Mattingly said. "It's one of those I won't really lose sleep over."
Kendrick doubled off Lilly to begin the frame and then stole third on a pitch in the dirt, which proved costly for the Dodgers.
"Those guys weren't holding me on and I had the green light there," said Kendrick, who scored all three runs for the Angels. "I think the pitch he threw was a changeup and I was able to take the bag. It does change the situational advantage. It takes away the ability to bounce breaking balls or certain pitches. We came up with a big hit there."
Belisario has allowed 11 of 17 inherited runners to score this season.
After beating the Angels twice at Dodger Stadium to begin the week, the Dodgers dropped a pair in Anaheim to fall to 18-53 in American League ballparks since 2005, the second worst Interleague road record in the Majors during that span. The Dodgers fell to 5-8 in games decided by one run and dropped to 0-19 when trailing after six innings.
"I didn't really feel like we played bad, we just didn't do enough to win it," Mattingly said. "We had a chance to win it, and we didn't do it."
Lilly had a chance to win his first game since last May but was unable to get Chris Iannetta with two out in the sixth after he was ahead in the count, 1-2. Lilly ended up walking the catcher and Mattingly removed him from the game.
"I didn't get the key out in the sixth there when I needed it," Lilly said. "I let that at-bat get away. I had him 1-2 and didn't put him away."
The left-hander had another solid start, but he still took the loss. Lilly was charged with three runs on five hits in 5 2/3 innings. He struck out three against three walks.
"Not good enough," Lilly said.
Unlike Wednesday's contest, when the Dodgers didn't have a baserunner until the fifth inning, Carl Crawford gave L.A. a spark with a triple to right to lead off the game. He scored on Adrian Gonzalez's sacrifice fly as the Dodgers gave Lilly an early lead, 1-0.
"I thought we had some momentum going and we just kind of didn't keep it going," Crawford said. "It's frustrating at the end."
Crawford made a sliding catch along the left-field line in the second and crashed into the wall. He said he hopes to play on Friday in Colorado, though he played with a sore back for the rest of Thursday's game.
"I feel like I ran into a truck or something," Crawford said. "I'm a little sore. That wall doesn't give. I just know we're kind of short on men a little bit, so I tried to fight through it. It's definitely one of those things you have to grind it out."
The Dodgers were short an outfielder with Matt Kemp placed on the disabled list before the game, the result of a mild right hamstring strain sustained during Wednesday's 4-3 loss.
Kemp's absence forced Andre Ethier to start in center field for only the second time in his career. Ethier appeared to be comfortable shifting over from right field, though only a few balls were hit in his direction.
Kendrick scored his first run on a double by Iannetta in the second to tie the game, 1-1. The second baseman tripled in the fourth, and came home on a single by Alberto Callaspo as the Angels went ahead, 2-1. Ramon Hernandez answered with a solo home run into the Angels' bullpen in the fifth to knot the game again. The veteran catcher entered the game hitting .111, but he also doubled in the second as the designated hitter.
But the Dodgers were unable to score again, and they head to Colorado for a three-game series looking to avoid their fourth losing skid of at least three games.
"At the end of the day, it's a collective thing and I think at some point we need to start just getting it done, one way or another," Lilly said.