Kennedy gave up a home run to Gregor Blanco in the third inning and Buster Posey's RBI single in the fifth before a strong sixth-inning performance.
After hitting Brandon Crawford with a pitch, Kennedy struck out Blanco and received help from Derek Norris, who caught Crawford stealing second to end the inning.
"He was outstanding, that sixth inning especially, getting it done," interim manager Pat Murphy said. "Norris gave him a big lift, strike 'em out and throw 'em out. For Ian the pitch count came up to 100 and he made some quality pitches to [Brandon] Belt.