Padilla (4-2) allowed just two hits and a walk while fanning six for the Dodgers, who took three games in this series and head into the All-Star break with a 49-39 record, two games behind San Diego in the NL West.
Jamey Loney hit a three-run homer and drove in four in the resounding victory.
Carlos Silva (9-3), who came into the game with seven straight quality starts, was hammered for six runs, six hits and three walks in just 1 1/3 frames before being ejected while arguing a call at first base. Silva came into the game 5-0 on the road this season and 3-0 against the Dodgers in his career.
Ryan Theriot doubled twice to account for half of Chicago's hits, and the Cubs, at 39-50, are 9 1/2 games off the pace in the NL Central.