The Dodgers' lead in the National League West over Arizona grew to 10 1/2 games while Boston fell back into a tie with Tampa Bay for the top spot in the American League East.
Nolasco (10-3) allowed just two hits and did not walk a batter while striking out six. He allowed a two-out single in the first and then retired 11 straight batters before hitting Daniel Nava with a pitch.
Kenley Jansen struck out two in a perfect ninth for his 21st save.
The game's only runs came on a two-out homer by Hanley Ramirez in the fourth after Carl Crawford had singled to lead off the inning. It was one of just three hits given up by John Lackey (8-11), who went the distance for the Red Sox while throwing a mere 97 pitches.
Los Angeles has won four in a row after sustaining back-to-back losses for the first time in almost two months. The Dodgers have gone 46-10 since June 21.
Celebrity Breakups and divorces of 2014 [PHOTOS]