Kershaw pitched like the No. 1 prospect in the Dodgers' organization that he's supposed to be, yielding just four hits and a walk while striking out five.
The Nationals did not get a baserunner to third, although Kershaw stranded three runners in scoring position.
"He deserved it," catcher Russell Martin said. "He's pitched in a couple games where he could have easily got wins. It's unfortunate it took this long for him to get it, but he got it and it's a good one, and hopefully from here he just keeps getting better."
Kershaw executed his game plan by getting ahead in the count and pitching aggressively, while using his off-speed stuff to keep the Nationals off-balance.
The rookie established his fastball and curveball early, Torre said, and mixed in a handful of changups while throwing an economical 86 pitches. Torre added Kershaw did not seem to be jumping at the hitters like he was during his five-run, 10-hit shelling at the hands of the Rockies on Tuesday in his first start since being recalled from Double-A Jacksonville.
Martin said Kershaw consistently located his fastball and commanded the glove-side pitch, which is in to righties and away from lefties.
"He was hitting that spot all day," Martin said. "He was throwing his curveball for strikes, and when he's throwing both those pitches for strikes he's going to be a tough guy to hit."
Kershaw has not pitched poorly, yielding three runs or fewer in six of his nine starts before Sunday, but a combination of a lack of run support and not going deep into games has prevented that first victory. He pitched six innings for just the second time on Sunday and has surpassed the 100-pitch mark just twice.
Kershaw was sent down to Double-A on July 2 after pitching well the day before at Houston, only to see the bullpen blow a 6-1 lead he left with in a game Los Angeles eventually won.
"I haven't pitched bad enough to not win, and at the same time this is what they expect from me, this is what I'm supposed to do up here," Kershaw said.
James Loney provided all the offense Kershaw needed with a homer in the second. The Dodgers later added a run with three straight singles in the fifth, including Martin's RBI hit.
The bullpen made sure it stood up with a scoreless inning each out of Chan Ho Park, Hong-Chih Kuo and Jonathan Broxton, who picked up his fourth save.
With the victory, the Dodgers reached .500 for the first time since May 30, when they were 27-27. They had lost five straight with a chance to get to .500.
"It's been at that slippery slope, but hopefully we can kiss it goodbye and start going north," Torre said. "We've been playing a lot better. The pitching we've gotten since we've been home has been more like what we got the first half, and to get this kid a win today was huge."
Added Martin, "We're not really worried about what our record is, where we are in the standings. We're just trying to play good baseball on a daily basis, and we just take it day by day, and if we keep playing like we're playing right now we're going to be way above .500."
On what was an otherwise feel-good day with the Dodgers winning their sixth in a row against Washington, Los Angeles got a bit of a scare when Nomar Garciaparra tweaked his left knee finishing off an unusual 5-3-6 double play in the fifth.
Lastings Milledge tried to go from first to third on a routine ground ball to third baseman Casey Blake, but first baseman Loney made an alert play throwing the ball across the diamond to shortstop Garciaparra covering third to finish off the double play.
Garciaparra left the game the next inning. Torre said Garciaparra could have played, but the manager did not think it would be "smart to try to push it."
Garciaparra is listed as day-to-day and will be re-evaluated on Monday. The veteran said he "feels halfway decent right now" and is not too worried despite his history of injuries.
"It wasn't an easy play, Loney made a great throw there," Garciaparra said. "He just slid in there. It was just kind of an awkward position when he slid in and kind of just got my leg and it just pushed my knee down, so it tweaked a little bit there."
Even with another injury scare from Garciaparra, this day belonged to Kershaw, the top prospect who finally gets to breathe a sigh of relief after recording his first Major League win.
"It feels great to get the win, personally get one under my belt, and hopefully there's more to come," he said. "It's done with. Win No. 2 now."