The Dodgers opened a new era under an ownership group featuring basketball great Magic Johnson and they had a successful start despite the unexpected departure of Kershaw after three shutout innings. The defending National League Cy Young Award winner was weakened by a bout with the flu and departed having allowed only two hits with three strikeouts.
He was replaced by Josh Lindblom, who went two perfect innings to get the win.
Los Angeles had a 3-1 lead when Kemp hit his eighth-inning homer, which turned out to be a vital blast when Cameron Maybin delivered a two-run homer for the Padres in the bottom of the inning.
Five Los Angeles pitchers combined to throw a five-hitter. Javy Guerra struck out one in a perfect ninth to get the save.
Guerra has been appointed the Los Angeles closer this season, two years after he saved 21 games in 23 chances for the Dodgers.
The loss went to Edinson Volquez, who made his regular-season debut for San Diego.