The victory pulled the fourth-place Dodgers to within 4 1/2 games of the first-place Rockies, their smallest deficit in the National League West since April 23. The Dodgers have won five of their last six games.
"The series sweep in D.C. was huge for our confidence, and now we know we're a good team," Taylor said, referring to the weekend sweep of the Nationals. "We're going to turn things around eventually, and now we can go out there and play free and easy, the way we're capable of playing."
Taylor's two-run shot to left-center, his sixth of the year, was followed by Puig's shot to left, his fifth, all in his last eight games. Both players homered off Bryan Shaw sliders.
Taylor and Puig were key contributors to last year's potent offense, but both are off to slow starts in 2018, with Taylor's OPS .754 and Puig's .687. Tuesday's homer was Taylor's first since May 4, although he's batting .303 in his last 10 games. Last year, the pair combined for 49 homers, with Taylor's OPS 850, Puig's .833
"It's been a grind for Chris. I know this is a weight off his shoulders," said manager Dave Roberts, who added that Taylor's return to the leadoff spot is only a matter of time.
All five of Puig's home runs have come after a 10-day stint on the disabled list, ostensibly for a bruised hip and toe, but also a chance for him to reset from an awful start to the season.
"I go to [the club's Arizona training facility], practice my swing, do everything I can do to help myself and get back to the team and play well," said Puig.
"He's getting his 'A' swing off more frequently," Roberts said of Puig.
Shaw took over in the sixth for Rockies starter Chad Bettis, who allowed two runs in the first inning and no hits the next four.
"The first one was very bad," Shaw said. "That's the pitch that, in your head you go, 'Please, don't hit it out of the park.' The second one was good. It was down, just a little more middle. With Puig, that's where his spot is. If I throw that four inches on the outer half, he pops out."
The Dodgers hoped to set the tone in a two-run, 34-pitch first inning against Bettis. A double by Justin Turner and an RBI single by Matt Kemp scored the first run. Kemp was doubled to third by Cody Bellinger, who rocketed a bouncer between the legs of first baseman Ian Desmond. Taylor and Puig walked on 3-2 counts to score the second run.
Colorado responded with Desmond's two-out solo shot in the second inning, then parlayed two-out singles from Charlie Blackmon, Gerardo Parra and Nolan Arenado in the third inning to tie the game at 2. Dodgers starter Brock Stewart escaped further trouble when Trevor Story was green-lighted 3-0 and flied out.
"When we're good, we get a lead and lose it, we come back, and that's what we did tonight," said Roberts. Stewart -- recalled for a spot-start necessitated by Saturday's doubleheader that doubled as a rotation tryout -- pitched evenly, charged with two runs on five hits in four innings that required 63 pitches. It was Stewart's fourth callup this season, the third this month. Roberts praised Stewart's willingness to do what's asked and said he did well enough "to get another opportunity."
"Someone's got to be that guy, up and down, here and there, helping out the team," Stewart said of his nomad role. "I'm happy to do it. Every outing in the big leagues for me, until I'm a mainstay, every outing is an audition for sure. It's exhausting, but I have everything in perspective. Not a huge deal."
MOMENTS THAT MATTERED After allowing a one-out double to Chris Iannetta in the ninth inning that brought up the tying run, Kenley Jansen got pinch-hitters David Dahl and Pat Valaika on a groundout and strikeout to earn his ninth save. In his last 14 innings, Jansen has 13 strikeouts and has allowed one earned run.
SOUND SMART Kemp cashed in Justin Turner's first-inning double with an RBI single and is hitting an MLB-leading .471 (16-for-34) with runners in scoring position. Kemp also preceded Taylor's homer with a leadoff single.
"Coming up through the Minor Leagues and my earlier days with the Dodgers, they always concentrated on hitting with runners in scoring position and getting ribbies," Kemp said. "I try to lock in and get the big hits."
HE SAID IT "Mom was giving me a hard time. She said when I was young and would dive for a ball, I would glide. Now I plop and stick. This time I made sure, I looked at the Jumbotron to see if I was gliding." -- Kemp, on utilizing defensive tips from his mother on a diving catch of Story's second-inning liner
UP NEXT Kenta Maeda will start Wednesday night's 7:10 PT series finale against the Rockies and lefty Kyle Freeland. Maeda is coming off a masterpiece of a two-hit shutout for eight innings in Miami. In seven career games against Colorado, the right-hander has a 0.88 WHIP.
Ken Gurnick has covered the Dodgers for MLB.com since 2001.