Jimenez, who entered with a 9.31 ERA, struck out four and walked one.
Travis Hafner hit a solo homer and had an RBI groundout for Cleveland.
Cory Luebke allowed a run, four hits and struck out six in five innings for San Diego.
Chase Headley and Everth Cabrera both hit solo home runs for San Diego. Cabrera also had an RBI triple.
Shin-Soo Choo had two doubles for the Indians.