Juan Uribe hit a three-run homer, Kershaw had an RBI double and the NL West-leading Dodgers improved to 25-3 after the All-Star break. They have won 19 of their last 20 road games and are 42-8 overall since June 22, the best 50-game stretch in the majors since the 1942 St. Louis Cardinals had the same record.
The previous team to win 19 of 20 road games was the 1916 New York Giants, according to STATS.
The 10-game winning streak is the longest for Los Angeles since an 11-game run in 2006.
Meanwhile, the skidding Phillies have yet to cross home plate since manager Charlie Manuel was fired Friday in the middle of a second-half swoon. They were blanked 4-0 by Zack Greinke and the Dodgers in Sandberg's debut and have now lost 21 of 25.
Both teams were .500 at the All-Star break.
Kershaw (12-7) allowed three hits and lowered his NL-best ERA to 1.80. He struck out eight and walked one.
Uribe singled and doubled before hitting a three-run shot to break the game open in the eighth inning.
The win was Kershaw's first in nine career games against the Phillies. The left-hander also helped himself at the plate with a run-scoring double. His seven RBIs lead the Dodgers' pitching staff.
Brandon League worked the ninth to secure Los Angeles' major league-best 16th shutout. It was the 12th time the Phillies have been blanked this season.
Philadelphia's lone threat came in the eighth, when Casper Wells doubled and John Mayberry Jr. walked with one out. But Erik Kratz popped out and after a wild pitch, pinch-hitter Carlos Ruiz struck out.
Kyle Kendrick (10-10) labored through six effective innings for the Phillies, yielding two runs and seven hits. He was aided by four double plays, including ones that ended the third, fourth and fifth innings.
The Dodgers opened the game with two singles and scored their first run when Mayberry let a grounder get by him at first base for an error. Los Angeles could have had more, but Andre Ethier grounded into bases-loaded double play.
Uribe and Kershaw hit consecutive doubles in the fifth to make it 2-0.
Domonic Brown got the Phillies' first hit in the fifth inning. He was later picked off first base.