Lilly (11-14) allowed four hits and fanned seven to move to 10-4 lifetime against the Padres.
Wade LeBlanc (4-6) surrendered four hits and had a career-high 10 strikeouts over seven innings, but the Padres couldn't build on their three-game sweep in Colorado.
"I don't think his velocity wavered through seven innings," Padres manager Bud Black said.
Jerry Sands doubled leading off the second and scored on a Russ Mitchell groundout.
San Diego left a runner in scoring position in the third and fourth frames, and Kemp went deep to right leading off the seventh. Kemp's homer was his 37th, tying him with St. Louis' Albert Pujols for the National League lead.
"I just have to relax, not try to hit home runs and try too hard," said Kemp, who is trying to become the first Triple Crown winner since Boston's Carl Yastrzemski in 1967. "I just relax and have fun. What ever happens is going to happen."
Cameron Maybin struck out looking to strand a pair of runners in the bottom half, but the Padres never mounted a late threat and struck out 12 times on the night.
Over the last seven games, Padres pitchers have allowed just nine earned runs...Sands extended his career-high hitting streak to 11 games...Dee Gordon extended his career-high hit streak to 10 games with a bunt single in the sixth for LA.