July 31, 2013, the Diamondbacks traded Kennedy to the San Diego Padres in exchange for relief pitcher Joe Thatcher, relief prospect Matt Stites, and a compensatory pick in the upcoming draft. Padres general manager Josh Byrnes was also the Diamondbacks' general manager when they had acquired Kennedy prior, and he referred to the pitcher as "the first guy I have ever traded for twice". The Padres immediately added Kennedy to their starting rotation, where he joined Andrew Cashner, Tyson Ross, Eric Stults, and Edinson Volquez. After being traded, Kennedy struggled on the road, going 0–2 in his first four away starts with a 6.95 ERA. In his worst outing of the season, Kennedy allowed six runs on eight hits in innings against the Pittsburgh Pirates. He posted a 4–2 record and a 4.24 ERA in 10 games with San Diego that season, striking out 55 batters in innings. Going into the 2014 season, Padres manager Bud Black placed Kennedy in the second spot of the starting rotation, between opening day starter Andrew Cashner and No. 3 Tyson Ross. On May 9, while facing the Miami Marlins, Kennedy not only tied his career-high 12 strikeouts as a pitcher, but he hit the first home run of his career, a solo shot against Miami starting pitcher Jacob Turner in the sixth inning. Over the course of the season, Kennedy saw noticeable improvement in his ERA, walks plus hits per innings pitched (WHIP), and strikeout-to-walk ratio over the previous season, which he credited to Black and pitching coach Darren Balsley, the latter of whom taught Kennedy to strengthen his leg kick when pitching to improve his command. Balsley's advice helped Kennedy add an extra mile per hour of velocity to Kennedy's fastball, which now reached speeds of and helped him strike out an average of 9.27 batters per nine innings. On September 27, while facing the San Francisco Giants for his 33rd and final start of the season, Kennedy passed his 200th inning pitched of the season for the third time in his career, and struck out his 200th batter of the season for the first time. He finished the year with a 13–13 record and a 3.63 ERA. While starting the Padres' 2015 home opener against the Giants, Kennedy had to be taken out of the game in the third inning with a left hamstring strain. He explained later that he had