MIAMI -- Marcell Ozuna hit his sixth go-ahead homer of the season and that was enough with the way the Miami Marlins' bullpen has been pitching lately.

Backed by Ozuna's three-run homer, Miami earned its fourth shutout of the season en route to a 3-0 victory over the Colorado Rockies on Sunday afternoon at Marlins Park.

The Marlins (37-32) have won the first three games of their series against Colorado (32-36). The set concludes on Monday.

With the win, the Marlins moved a half-game ahead of the New York Mets for second place in the National League East. The Mets were swept by the last-place Atlanta Braves this weekend, and the Marlins are five-games over .500 for the first time this season.

"We're playing (well)," Ozuna said. "(Manager) Don (Mattingly) had a meeting with us in San Diego (after a loss on Wednesday). ... This is the result."

Whatever was said must have worked.

Miami broke up a scoreless tie in the seventh inning. Derek Dietrich walked and Martin Prado singled before Colorado starter Tyler Anderson (0-1) struck out Christian Yelich for the second out of the inning.

However, Rockies manager Walt Weiss removed the left-handed Anderson and replaced him with right-hander Miguel Castro, who allowed Ozuna's 13th homer of the season. On a 2-0 pitch, Ozuna pulled a 95-mph fastball over the fence in left-center.

Weiss said Anderson, who had thrown 102 pitches - a career high including the minors - was never going to be allowed to face Ozuna in that spot.

"Ozuna mauls left-handed pitching," Weiss said.

So while the decision to go to the bullpen was solid, Weiss said, there was something off about Castro.

"He wasn't getting around the ball," Castro said. "You could tell on the first slider he threw to Ozuna. It got away from him, arm-side. That happens from time to time with Castro. The stuff is electric. But you have to get in good counts.

"(Castro is) a back-end guy. That's a matchup (against Ozuna) we were looking at since the start of the inning. That was the matchup we wanted. But Castro got in a bad count and threw a flat fastball."

Added Ozuna: "The pitch was in the right spot to hit it hard."

Ozuna's homer helped give the win to Tom Koehler (6-6), who pitched six scoreless innings before departing for a pinch-hitter to start the fateful seventh. Koehler struck out six and allowed just two hits but walked a career-high six batters, including one intentionally.

Three of his walks were to Daniel Descalso, who tied his career high for bases on balls in one game.

"Today was a grind from the beginning," Koehler said. "It's not the best I've thrown a baseball, but I was able to make some pitches."

Miami's bullpen, which has been outstanding lately, worked the final three innings. Kyle Barraclough pitched the seventh, David Phelps picked up his NL-leading 17th hold in the eighth and A.J. Ramos ran his streak of consecutive saves to 22.

In addition, the Miami bullpen has gone 15 innings in a row without allowing a run. Marlins relievers have allowed just two hits during that span.

"They've got a good bullpen," Weiss said. "They have a knack for finding those power arms and putting them in the bullpen. They certainly have a nice bullpen right now."

NOTES: Colorado put RHP Tyler Chatwood (back) on the disabled list. RHP Scott Oberg was recalled from Triple-A Albuquerque. RHP Eddie Butler will move from the bullpen to replace Chatwood in the rotation. Oberg is a reliever. ... Miami optioned LHP Justin Nicolino (2-4, 5.17 ERA) to Triple-A New Orleans. Miami selected the contract of RHP Paul Clemens from New Orleans. Clemens was 6-4 with a 4.30 ERA and two complete games in 14 starts at New Orleans. In 48 appearances in the majors, Clemens, 28, is 4-8 with a 5.51 ERA. ... Nicolino, 24, hasn't won a game since May 3. He went seven straight games without lasting at least six innings. ... Colorado hopes LHP Jorge De La Rosa (3-4, 7.61 ERA) is back on track after winning his previous start, pitching five scoreless innings against the New York Yankees. De La Rosa, Colorado's career wins leader (81), starts the series finale on Monday against Clemens.