Colorado has won 10 of 12 to reach the .500 mark. The surprising Rockies moved within 3 1/2 games of the second NL wild card, with three teams between them and Miami.
The win took some of the sting off news that rookie shortstop Trevor Story will likely miss the rest of the season because of a torn ulnar collateral ligament in his left thumb. Story's 27 homers lead the NL and are the most by a rookie shortstop in National League history.
Josh Reddick went 0 for 4 in his Dodgers debut but made a difference in right field. He made a diving catch of Charlie Blackmon's sinking liner in the seventh and threw out Gonzalez at the plate in the eighth.
Reddick was acquired from Oakland on Monday in a five-player trade, leading to the demotion of outfielder Yasiel Puig.
Puig was sent to the minors. General manager Farhain Zaidi said Puig has 72 hours to report to Triple-A Oklahoma City and is expected to be there by the weekend.
The Rockies scored a run in the third and added three more in the fourth with only one hit. Brandon McCarthy (2-2) walked the first two batters of the inning and was lifted for Luis Avilan, who allowed both runners to score and another one in on Gonzalez's groundout that made it 4-0.
Gray (8-4) struck out six and allowed just two hits but needed 96 pitches to get through five innings. He worked around a 38-minute rain delay in the first.
Colorado scored three more off reliever Jesse Chavez, who made his Dodgers debut after coming over in a trade with Toronto on Monday. Gonzalez knocked in two with a double.
Turner spoiled the shutout with a two-run double in the eighth. Grandal hit a solo homer, his 16th, in the ninth.
Dodgers: LHP Rich Hill (hand) did some long tossing and will throw a bullpen Wednesday. Hill, who came to the Dodgers in the deal that included Reddick, might go out for one rehab start before making his Dodgers debut.
Rockies: RHP Chad Qualls (colitis) threw 18 pitches on the side. He is scheduled to throw a bullpen Wednesday. ... OF Gerardo Parra (ankle) is progressing and could be activated soon. He has been out since June 15.
Four fans jumped over the wall along the first base line and rushed the field carrying signs in the top of the seventh inning. They were tackled by security personnel before they could reach any players and were taken off the field.
A press release from Direct Action Everywhere, an animal rights group, claimed that the four people were activists with its group and carried signs that said "Dodgers Torture Animals" and "Keep Animal Cruelty Out of Sports."
The Dodgers have not announced who will pitch against Colorado LHP Tyler Anderson on Wednesday. Anderson (3-3, 3.33 ERA) allowed one run in six innings during Colorado's win over the New York Mets on Thursday but didn't get a decision.