The 22-year-old Kelly was the key player among the four obtained from the Boston Red Sox in the trade for Adrian Gonzalez on Dec. 6, 2010.
Kelly also got his first big league hit, a single up the middle with two outs in the fifth. The Padres loaded the bases before Chase Headley struck out.
Kelly (1-0), promoted from Double-A San Antonio earlier Monday, allowed three hits in six innings, struck out four and walked two. He was out from April 12-July 23 due to a strained right elbow.