Kershaw (21-5) gave up two runs and scattered four hits to win his eighth straight decision. He fanned six and issued only one walk and hasn't lost since August 7 at Arizona. His 21 victories are the most for a Dodger since Orel Hershiser had 23 in 1988.
"It's completely out of my control. I can't do anything about it," Kershaw said of the possibility of winning the Cy Young Award. "It's been an awesome year, it's just unfortunate we didn't make the playoffs."
Kershaw is also close to becoming the 31st overall and 16th NL pitcher to win the triple crown since 1900. He is tied with Arizona's Ian Kennedy in wins, paces the majors with a 2.28 ERA and has an NL-best 248 strikeouts.
Javy Guerra closed out the Padres in the ninth to seal the win.
Kemp's attempt to win the triple crown took a hit Sunday as he went 1-for-5, dropping his average to .324, which is nine points below Milwaukee's Ryan Braun. Kemp, who leads the NL in RBI with 120 and is tied with St. Louis Albert Pujols in homers with 37, has a tall task ahead of him.
Boston's Carl Yastrzemski was the last player to lead the league in average, home runs and RBI, while there hasn't been an NL triple crown winner since Joe Medwick accomplished the feat for St. Louis in 1937.
Corey Luebke (6-10) gave up four runs -- three earned -- on five hits over six innings of work.
The Dodgers opened the scoring in their first at-bat when Jamey Carroll drew a one-out walk and Kemp brought him home with a double to center. Miles then singled home Kemp for a 2-0 lead.
Los Angeles added two more runs in the fifth to expand the lead to 4-0. Carroll walked and Kemp reached on an error by Gonzalez. Juan Rivera knocked in Carroll with a single to left and Kemp scored on a fielder's choice by Miles.
San Diego got on the board in the home half of the inning thanks to a solo- shot from Cunningham to make it 4-1.
"I was waiting for a fastball...and I just got the barrel to it somehow," Cunningham said.
the Dodgers came right back with a pair of runs in the eighth courtesy of a two-run homer by Barajas to give Los Angeles a 6-1 advantage.
The Padres pulled a run back in the home half of the eighth when Orlando Hudson ripped a double and came around to score on a triple by Gonzalez to account for the final margin.
With the victory, the Dodgers have won nine of their last 10 series...Kershaw is 3-0 with two complete games against the Padres this season...Los Angeles took the season series with San Diego, 13-5.