In the opener, the Dodgers committed four errors and wasted four hits from Ramirez while losing, 6-4.
Capuano (2-4) struck out four without issuing a walk, and only one of the three hits he allowed left the infield. He lost his starting job over the winter with the signings of Zack Greinke and Hyun-Jin Ryu and spent two stints on the disabled list, but he's survived to reclaim his role in the rotation.
Capuano said fastball command was his key weapon in taming an offense that beat Ryu earlier in the day.
"I was just trying to keep it down, and it had a lot of movement on it, so even when I didn't locate it, it still had pretty good movement on it and I was able to get ground balls," Capuano said.
"I've gone up with him in the Minor Leagues and the big leagues, so I know that if he's keeping the ball down, he's pretty effective," said Yankees first baseman Lyle Overbay.
Coming off only one four-inning, 58-pitch rehab start in which he said he felt some tightness, the left-handed Capuano extended his arm to 84 pitches in his first official start since May 29, when he strained his left lat muscle. He had been on the disabled list previously with a strained left calf muscle he sustained during the Dodgers' April 11 brawl in San Diego.
"I'm not surprised he pitched good, but I am with how long he went," said Mattingly. "He was feeling great and we got an extra inning, and he really wanted to go back out. But not knowing what we'll get the next few days, we saved some bullets so if he has to bounce back quick he's able to do it."
Mattingly said that doesn't mean Capuano would be wheeled back on short rest for Sunday's game, as that starter remains unannounced and will likely be callup Matt Magill.
Puig, who had three hits in Game 1, had two more in the second game (including a home run) for a total of 27 hits in his first 15 games to tie Yankees legend Joe DiMaggio and Terry Pendleton as runners-up on the all-time list. Milwaukee's Irv Waldron in 1901 and St. Louis' Bo Hart in 2003 had 28 each.
In the two games, Puig went 4-for-9, Adrian Gonzalez went 4-for-9, Ramirez went 6-for-8 and Andre Ethier went 2-for-6.
"It's a good sign and I hope something of a trend," said Mattingly. "Let's see where we go with it. [Puig] and Hanley with Adrian give us a good little grouping, and Andre is starting to swing the bat. We're starting to look like the group we talked about early in the year."
And that's with Matt Kemp and Carl Crawford still healing from hamstring injuries.
"It's going to get better when Matt gets back, so we've just got to hang in there and keep playing a little bit better, each player, and keep bringing the team together," said Ramirez, who has played only 15 of the Dodgers' 70 games because of right thumb surgery and a strained left hamstring.
The Dodgers gave Capuano an immediate lead against Phil Hughes in the second game with the first four batters singling -- a line drive by Skip Schumaker, a perfect bunt by Puig, another line drive by Gonzalez for the first run and a sharp ground-ball single to right by Ramirez for the second run.
Gonzalez scored the third Dodgers run in the third inning when he doubled, advanced to third on Ramirez's flyout and was doubled home by Ethier.
Ethier made a big defensive play, and Robinson Cano a baserunning mistake, in the fourth after Jayson Nix's leadoff infield single. Cano tried to stretch a single into a double, but Ethier threw him out at second for the first out of the inning with Nix taking third, where he was stranded.
Puig created a rally in the fifth after being hit on the left hip by a Hughes pitch leading off. Puig stole second, went to third when Gonzalez bounced to the right side and scored on Ramirez's broken-bat single. Ethier singled Ramirez to third and scored on Jerry Hairston Jr.'s sacrifice fly.
"He's a great hitter, lots of power," Gonzalez said of Ramirez. "He's just a guy you definitely want in the lineup, so it's great that he's back in there doing what he does and giving us another bat in there that can help us score runs."
Puig added to the Dodgers' lead when he slugged the first pitch of the seventh inning by Adam Warren to the opposite field for his fifth home run since his June 3 promotion from Double-A Chattanooga. Puig's five home runs are tied for third on the club.
"I see the breaking ball outside and really liked it," said Puig.