He's been going strong all season, with his only defeat a 2-0 loss at Tampa Bay.
The Angels' left-hander held the Dodgers to two runs on five hits, with two walks and one strikeout.
"Joe did an outstanding job," Angels manager Mike Scioscia said.
Dodgers manager Joe Torre agreed.
"He looked like he was having an easy time doing whatever he was doing," Torre said. "Up until the base hit and the home run, it just looked like he was pretty much putting the ball where he wanted and we really didn't put any pressure on him."
Saunders, who has taken up a lot of the slack created by injuries to John Lackey and Kelvim Escobar, held the Dodgers to two runs - on Andre Ethier's two-run homer in the seventh - in 7 1-3 innings. He gave up five hits, walked two and had one strikeout.
"He's a very deceptive pitcher," Ethier said. "He has a good fastball and good off-speed stuff, and he's real deceptive with his delivery. "His pitches just happen to move a little bit at the point of contact, enough to throw hitters off and keep guys off-balance so they can't square up too many balls."
The loss continued the Angels' edge over Torre. They had a 61-55 record against the Yankees while he was the New York manager, the only AL team with a winning mark against them, and eliminated them from the playoffs in 2002 and 2005.
The win also continued the Angels' recent success against the Dodgers; they've won eight of the last nine, gone 15-3 in the last 18 meetings in Anaheim, and lead the all-time series 36-27.
Scot Shields replaced Saunders with a runner on second and one out in the eighth and retired the next two batters, then Francisco Rodriguez pitched a perfect ninth for his major league-leading 17th save in 18 chances.
"I never want to come out, but we've got a couple of the best guys, at setup and closer, in baseball," Saunders said.
The Dodgers' Hiroki Kuroda (1-3) allowed four runs, three earned, on seven hits and two walks in 6 1-3 innings. He struck out five.
"Kuroda, I thought pitched very well," Torre said. "We haven't scored many runs for this guy, so every single pitch he throws, there's a lot attached to it. We don't give him any breathing room. But he was right on it tonight."
After Ethier hit his fourth homer of the season to trim the deficit to 3-2, the Angels answered with a run in the bottom half.
Vladimir Guerrero, who provided the Angels' second run of the game with a sacrifice fly, drove in their fourth with a grounder to third. Maicer Izturis, who had walked and advanced to third on two wild pitches by Kuroda, slid into the plate safely when third baseman Russell Martin fielded Guerrero's grounder and bounced his throw to the plate.
The play was ruled a fielder's choice, no error involved, and Guerrero was credited with the RBI.
The Angels took a 3-0 lead with a pair of runs in the fifth, on Guerrero's sacrifice fly and Garret Anderson's RBI single.
The Angels scored their first run on a fluke play in the fourth inning, starting after Casey Kotchman hit a ground-rule double down the left-field line with two outs.
Kuroda then struck out Erick Aybar, but catcher Gary Bennett couldn't cleanly handle the third strike that was in the dirt, and his throw to first sailed over first baseman James Loney's head for an error. Kotchman scored on the play.
Martin, the Dodgers' regular catcher, started at third for the second game in a row in place of Blake DeWitt, out with a sore lower back. That gave Bennett his second consecutive start behind the plate.
Notes: The Dodgers have won only four times in their last 28 interleague games on the road. ... The Angels went 14-4 in interleague play last season to tie Detroit for the best record in baseball. Included in the Angels' mark was a 5-1 record against the Dodgers.