But the Dodgers mounted a threat in the ninth against San Francisco's Sergio Romo (3-4), loading the bases with one out.
Kershaw (8-5) logged a third win in three starts, limiting the Giants to one run on three hits over eight innings. The left-hander walked one and struck out three.
Kenley Jansen recorded his ninth save for Los Angeles, which took the rubber match of a three-game series and improved to 12-3 in its last 15 games.
Gaudin was saddled with a hard-luck no-decision after yielding just one run on four hits over seven frames, striking out nine.
Andres Torres supplied the only RBI for the Giants, who lost for the 13th time in 16 contests.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut