Billingsley pitched into the eighth and combined with two relievers for a four-hitter. The Dodgers, playing their second game without hitting star Andre Ethier, won for the 12th time in 15 games.
"We got about everything we could today out of what offense we put together," manager Joe Torre said. "It was all about pitching."
Los Angeles' only other hit was a seventh-inning single by Ronnie Belliard.
After entering the weekend with a 3 1/2-game lead, the Padres' margin atop the NL West is down to a half game over the San Francisco Giants, who come in for a two-game series starting Monday night. The Dodgers are two games back.
"This was a big series," Torre said. "It's a big win because we put a streak together ourselves where we've played good baseball and had good pitching. That's where we were fumbling around early on trying to get that good feel. Over the last 10 days, I guess, we've played a lot better."
The Dodgers went 6-0 on a swing through Arizona and San Diego, their first perfect road trip of more than three games since the final trip of 2006, when they were 6-0 at Colorado and San Francisco.
Billingsley (4-2) shut down the Padres over 7 1/3 innings, allowing just four singles, striking out six and walking one. Jonathan Broxton pitched a perfect ninth for his third save in the series and his seventh overall in nine chances.
"He was great," Torre said of Billingsley. "He was so comfortable to watch for me. He had a good tempo all game. He didn't try to rush himself."
Wade LeBlanc held the Dodgers hitless until Martin hit a line shot that zipped past both the left-hander's head and diving second baseman David Eckstein and into center field for a single with one out in the sixth. It scored Jamey Carroll, who drew a leadoff walk and was sacrificed by Billingsley.
Martin extended his hitting streak to 11 games.
"I was hoping it would hit me," LeBlanc said. "It wasn't close to my glove, but I was hoping it would hit me and land on the mound. I saw it off the bat. I was hoping some part of my body could get in the way of it."
Ethier has a fractured top knuckle on his right pinkie, which will need to be immobilized. He headed back to Los Angeles on Sunday morning to be examined by a hand specialist. The Dodgers aren't sure how long he'll be out.
So while Blake and Ramirez sat, Martin played.
"I think he thinks I'm joking when I tell him I want to play," Martin said, referring to Torre. "The more I get in there, the better I feel at the plate, the better feel I have for the game. He just trusts me to let him know when I really do need a day off."
LeBlanc (2-1) allowed only two baserunners the first five innings, both on walks, and one of them was erased in a double play. He finished with one run and two hits in seven innings, four strikeouts and three walks.
"I blinked," LeBlanc said. "I was trying to keep up with Billingsley and trying to make the pitches that he was making and I blinked."
San Diego Chargers GM A.J. Smith sat in the fourth row behind home plate. His daughter, Andrea, is manager of Petco Park suites. Before the game, Smith met his counterpart with the Padres, Jed Hoyer. ... Padres OF Scott Hairston sat out a day after tweaking a hamstring. ... All three games of the series were sellouts. The total attendance of 126,819 was the sixth-highest total for a a weekend series in Petco Park's seven-year history.