Juan Uribe also had four hits, scored two runs and drove in a pair for the Dodgers, who will look for a sweep of the three-game series in the nightcap. Miguel Olivo and Andre Ethier each had two hits for Los Angeles, which got a solid effort from starting pitcher Dan Haren.
Haren (4-0) got the win, allowing four runs -- three earned -- on six hits over 6 2/3 innings. The right-hander struck out seven and walked three, picking up his fourth win in six starts this season.
"I felt really good," said Haren. "I was in command. I had a good rhythm. ... Obviously it was nice getting all those runs."
Brian Dozier had two hits and drove in two runs for the Twins, who have lost three of four during their eight-game homestand.
Trailing 5-2 in the fifth inning, the Twins got a rally going, but it was ultimately squashed by a replay.
Minnesota got a pair of runs back when Dozier singled home two. However, he was later doubled off second base after a line-drive by Trevor Plouffe that was caught by Hanley Ramirez at short and then tossed to Gordon covering second.
Los Angeles later put the game out of reach with a three-run seventh. Uribe's ground-rule double scored the first run. Olivo followed with an RBI single and Uribe scored the final run of the frame on a Carl Crawford base hit.
The Dodgers added an insurance run in the ninth when Either scored on Olivo's sac fly.
Los Angeles has now won six straight interleague road games.
The Twins got two runs in the first off Haren. The first came when Joe Mauer scored on a Kubel base hit and the second scored on the same play as Trevor Plouffe came home on a pair of throwing errors.
The Dodgers went ahead in the second with three runs off Minnesota starter Mike Pelfrey. Uribe scored on a Dee Gordon fielder's choice ground out and Puig followed with a two-run double for the one-run edge.
Los Angeles added two more runs in the third. Matt Kemp doubled home the first run of the frame and later scored on a Uribe single for a 5-2 cushion.
Pelfrey (0-3) was hit with the loss, lasting only four innings and being charged with five runs on seven hits. The right-hander struck out two and walked three, tossing 85 pitches over the four frames. Hiss ERA went from 7.32 to 7.99.
"I've had bad stretches before but I don't think it's ever been a stretch of not being able to throw strikes," said Pelfrey. "In that aspect, this is a little bit newer. I still need to go out there and give this team a chance to win but obviously I'm not doing that right now."