Kuroda (7-13) was the subject of trade rumors leading up to the July 31 deadline. But he informed the club that he would use his no-trade clause and block any deal to another team, preferring to finish the season with the Dodgers.
In ending his four-game losing streak, Kuroda allowed four hits while striking out eight and walking two. It was his second strong outing in San Diego this season, as he also shut out the Padres in April.
"After I made the decision, I still thought about if I made the right decision or not, but it really pays off when you get a win like this," Kuroda said through an interpreter. "It's great to get a win with this team."
The Japanese right-hander's teammates provided just enough run support. They also showed strong support when he chose to remain with the team and finish out the final year of his contract.
"Given the situation with the team, I had some thoughts about leaving," Kuroda said. "I thought maybe it would be better for the team if I left, but when I saw my teammates' reaction, they were really happy that I stayed, so I think I made the right decision."
Kemp drove in his NL-leading 84th run as the Dodgers beat San Diego for a fifth consecutive time. The center fielder also made a strong defensive play in the ninth, snaring a fly ball off the bat of Aaron Cunningham.
"It's the same, he's been so good," Dodgers manager Don Mattingly said of Kemp. "He's just grinding away. That's what we talked about, just keep grinding at-bats and at the end of the year, there's going to be a pile of numbers there. Just stay focused."
Latos (5-11) went seven solid innings while yielding one run, and was pulled for a pinch-hitter in the seventh.
Dee Gordon beat out a bunt single to lead off the fourth against Latos and advanced to third on two groundouts before Kemp drove a single to left.
"I wanted to throw a fastball down in the lane and make (Kemp) hit it to the deepest part of the ballpark," Latos said. "I kind of got around it and it was up a little bit and found a hole. Maybe if I don't give up a run it's 0-0 and we're still playing and with a chance to win the game.
Gordon, recalled from Triple-A Albuquerque on Sunday, also singled and stole a base in the first.
"I'm just trying to get on base," Gordon said. "I know when I lead off, I want to try to see more pitches. I just try to get on and do what I can."
Dodgers reliever Mike MacDougal allowed the tying run to reach third base in the eighth after giving up two singles, but recovered to retire the next two batters and preserve the lead.
Javy Guerra converted his ninth save in as many chances with a perfect ninth.
Latos gave up six hits while striking out six, including four of the first nine batters in the game, and did not issue a walk.
"I've been stringing my pitches together better and attacking hitters," Latos said. "Everything felt good."
The shutout was the Dodgers' 13th of the season. San Diego has been held scoreless 16 times this year, including nine times at Petco Park. The Padres have lost by 1-0 scores three times to the Dodgers this year.
"It was a well-pitched game by both guys," Padres manager Bud Black said. "Kuroda was solid, Mat matched him. They snuck one across. We mounted a couple threats and couldn't get that hit to tie the game or take the lead."
Blake Tekotte was the lone bright spot for the San Diego offense, getting three hits in his first game since being recalled from Double-A San Antonio. He also stole two bases.
Padres RHP Dustin Moseley will undergo season-ending surgery on his left shoulder on Wednesday. He was placed on the DL on July 26 after dislocating his non-throwing shoulder. ... San Diego's Will Venable pinch-hit in the seventh and remained in the game in left field after not playing since Friday due to back spasms. ... The Dodgers have not announced who will fill the fifth spot in their starting rotation after Rubby De La Rosa went on the DL on Monday and will undergo season-ending elbow surgery. ... Dodgers OF Andre Ethier did not play in the game strictly as a day off, Mattingly said. ... Tim Stauffer starts for the Padres on Wednesday night to attempt to salvage a sweep by the Dodgers. Stauffer has faced LA twice this season, going 0-1 with a 2.84 ERA. Ted Lilly opposes Stauffer for the Dodgers, bringing an 8-3 record and 2.93 ERA versus San Diego.