Lester (12-7) controlled the Dodgers on three hits, working around four walks and striking out six before leaving with a 4-0 lead.
After the Red Sox bullpen allowed two runs, Koji Uehara retired the final four batters for his 13th save as Boston recorded its first-ever victory at Dodgers Stadium.
The Red Sox came into the game tied with Tampa Bay atop the American League East.
Hyun-Jin Ryu (12-5) was touched for four runs on five hits in a five-inning start for NL West-leading Dodgers, whose four-game winning streak was snapped.
Adrian Gonzalez drove in two runs for Los Angeles.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes