Capuano (5-6) allowed three hits and two walks with five strikeouts to win consecutive starts for the first time since April 2007.
"Right now, I feel like I'm making good pitches," said Capuano, who missed 2008-09 seasons while going through Tommy John surgery and rehabilitation.
Capuano has allowed one earned run or fewer in three of his past four starts.
"I feel like I'm able to throw the ball where I want, and I've got my velocity up to level where my changeup is effective off that fastball, so I'm just trying to just execute pitches."
Reyes had three hits for his majors-leading 33rd multi-hit game, homering two pitches after pinch-hitter Scott Hairston also did in the ninth. David Murphy and Angel Pagan went 2 for 4 and Carlos Beltran had a two-run single for New York, which has won six of eight.
Reyes is 8 for 15 with five runs in the series. Two of his three home runs have come in the past three games. His .346 average leads the majors.
"Right now, I've got everything working, and I've been consistent with everything, so hopefully I can continue," Reyes said.
"I feel very good right now, very confident."
Reyes leads the National League in hits and is among the top three in runs, total bases, doubles, triples and steals.
"Obviously, I get to see him everyday, and in mind my mind the answer to (whether he's the NL MVP to this point) would be yes," Mets manager Terry Collins said.
"As a matter of fact," Collins added, joking, "we blamed him for the slow start we had because he didn't get on the first at bat."
Kevin Correia (8-5) was perfect through 4 2/3 but unraveled late. He missed on a chance to tie for the majors' lead in victories.
The game was scoreless through six innings. The Mets scored one in the seventh and four in the eighth.
Correia retired the first 14 batters he faced before Jason Bay's two-out single through the left side of the infield in the fifth. He ultimately was charged with four runs on seven hits in 7 2/3 innings.
"Early on, he was very tough, but for us to stick with it and give good at bats one right after another, that's what kept us in the ballgame," Hairston said. "Chris Capuano as well. Once we scored a couple runs, we kept adding and piling on. That's what good teams do."
Pittsburgh's Andrew McCutchen had two hits, extending his hitting streak to 11 games. The Pirates again failed in a chance to reach .500 in June for the first time since 2005.
Pittsburgh doubled off Angel Pagan because he didn't step on second on his way back to first on Bay's sacrifice fly in the seventh.
The Mets made any potential controversy moot with the help of six consecutive two-out hits in the eighth.
Correia gave up a single to pinch-hitter Willie Harris. Reyes singled and Justin Turner hit an RBI double before Beltran's two-run single off of Chris Resop. Daniel Moskos came on, and Murphy and Pagan singled. The latter hit drove in pinch-runner Jason Pridie.
"I felt I had a really good outing until two outs in the eighth inning," Correia said. "I just couldn't get that last out, and that was disappointing."
Another odd play happened in the bottom of the seventh. Lyle Overbay led off with a fly to the center field wall. Pagan leaped to catch it, but fireworks that typically follow a Pirates home run at PNC Park went off.
It clearly was not a home run -- replays, however, brought into doubt whether Pagan caught the ball or trapped it after it bounced off the wall.
Pittsburgh manager Clint Hurdle came out to argue, and he was ultimately ejected -- by two umpires. Jerry Layne was "credited" with the ejection, as his signal came a moment before Bob Davidson's.
"I had some extra time to watch the replay, and the ball was off the wall," Hurdle said. "They missed the call, and I'm sure they will think they didn't miss the call until they see the replay. It's a hard call to make, and they miss a call now and again. It happens."
Correia also had the Pirates' only extra-base hit of the game, a two-out double in the fifth. ... Capuano retired the final seven batters he faced. ... Hairston's home run, his second, was the Mets' third pinch-hit homer of the season. ... Pirates INF Josh Harrison was not in the lineup due to tightness in his right oblique. It is not expected to be serious. ... McCutchen's hitting streak is the longest by a Pirates player this season.