Rollins and Yasiel Puig opened the game with back-to-back doubles off Reds starter John Lamb for the Dodgers' first run. Turner's one-out homer in the third inning, his 15th, followed a double by Adrian Gonzalez. Rollins homered off reliever Ryan Mattheus in the sixth, his 13th.
The Reds, who have lost 10 of 11, scored a two-out run in the sixth with a single off winning starter Alex Wood (9-8) and the second double of the game by Todd Frazier, this one off reliever Chris Hatcher.
"Honestly, I waited a hitter too long," manager Don Mattingly said of removing Wood with a shutout. "Todd's first two times up he was right on the pitches. This was more about his swings and the respect we have for him. He wasn't going to get Frazier again. I didn't feel he had enough to get back through Frazier again."
Hatcher was the first of five Dodgers relievers who finished up the final 3 1/3 innings without being charged for a run, although Juan Nicasio returned from the disabled list and loaded the bases with two outs in the eighth. Luis Avilan came on to strike out Jay Bruce and put down that threat.
"It was the biggest out of the year, because our season started tonight," said Mattingly.
MOMENTS THAT MATTERED Dodgers defense: The Reds had runners on base in five of Wood's six innings, but the Dodgers turned two double plays, and Puig made a running catch in the right-center gap to rob Jason Bourgeois of an RBI extra-base hit to end the fifth inning. The infield turned a third double play behind J.P. Howell in the seventh inning.
Frazier drives in a run: It was 5-0 in the sixth, when a Brandon Phillips two-out single finished Wood's night. Frazier ended the Los Angeles shutout bid with his RBI double, on which Phillips scored with a headfirst slide as the throw home went over the catcher. Frazier also hit a leadoff double in the second inning, but he was left stranded.
Howell, Avilan put out fires: After Frazier's RBI double, Howell came on to retire Bruce on a grounder to first baseman Gonzalez and end the threat. Bruce was again the escape hatch for the Dodgers to end the eighth, when Avilan came on to strike him out with the bases loaded. The Reds were 0-for-7 with runners in scoring position.
"We got enough outs tonight," said Mattingly. More >
LeCure smooth again: Reds reliever Sam LeCure took over in the eighth inning and retired the side in order with groundouts sandwiching a flyout to right field. LeCure has worked five scoreless innings in his three appearances since returning to the big leagues from a season-long stint at Triple-A Louisville. The right-hander has retired 14 of his 15 batters faced, with one walk.
"He said he had a four-hit shutout. It was a pretty good case." -- Mattingly, on what Wood said trying to stay in the game
"It's a disappointing night in regards to going out there and starting the team off in a hole, 1-0, early. It's part of the game. I feel like keeping the strike zone established was a struggle for me tonight." -- Lamb on his start, in which he allowed three earned runs and five hits over five innings, with three walks and six strikeouts, while throwing 108 pitches. More >
WHAT'S NEXT Dodgers:Brett Anderson starts the second game of the three-game series Wednesday at 4:10 p.m. PT, coming off a loss in Houston, where he allowed three runs in six innings. With an almost identical line, Anderson was the winning pitcher against the Reds at home on Aug. 15, his first career start against Cincinnati.
Reds: Facing Anderson for the second time this month will be David Holmberg in the 7:10 p.m. ET game on Wednesday. Holmberg lasted five innings but allowed five earned runs and 11 hits on Friday vs. Arizona. At Los Angeles in the Aug. 15 meeting, he lasted only two-plus innings and gave up seven earned runs, including three homers.