The Rockies, who had won four of the previous six games during this homestand, had a decent offensive output in six innings against Marlins righty Henderson Alvarez (10-5) -- 10 hits, including two-run homers from Justin Morneau (his first in 130 at-bats) and Corey Dickerson. Nolan Arenado had his second four-hit performance in three games, and DJ LeMahieu ended a 4-for-61 skid with three hits.
All the Rockies needed was for the bullpen to feed off the momentum from Brown, who replaced scatter-shot starter Franklin Morales (5-7) with the bases loaded and no outs in top of the fifth.
Brown forced an Ozuna grounder, walked Jarrod Saltalamacchia to push in a run, and extracted the double play from Adeiny Hechavarria.
In the bottom of the fifth, Dickerson ended an 0-for-10 slump by launching his 18th homer of the year to cut the deficit to 6-4. But the poor relief pitching the rest of the way didn't give the Rockies a chance.
"When Brown got out of that jam, I felt like we were going to win that game," Rockies manager Walt Weiss said. "I thought we had put together a lot of good at-bats against Alvarez, who is having a good year. I thought we would find a way to win that game. Obviously, we didn't get it done."
Matt Belisle walked three and gave up one run -- all with two outs in the seventh. Boone Logan gave up four runs on one hit, two walks and a hit batter, and Juan Nicasio served up the slam to Ozuna, who improved his homer total to 19.
Only Brown and Nick Masset, who gave up two hits but struck out two, managed to escape without giving up runs. Until Ozuna's homer, the Marlins spent the night taking their walks and making sure outs were productive.
It wasn't the sexiest offensive performance, but it was good enough for the Marlins, a surprise National League Wild Card contender, to peek above .500 (64-63). The Marlins' 20 wins since the All-Star break are more than any NL team except the Nationals (22).
Morales went four innings plus four batters in the fifth and gave up six runs on eight hits and two walks. Two runs scored on sacrifice flies by Alvarez and Ozuna, another on Donovan Solano's fielder's-choice grounder and one more when Casey McGehee ended Morales' night by drawing a bases-loaded walk.
"They played a good team game," Morales said. "What I tried to do was make my pitches and tried to get a ground ball, but sometimes I missed my pitches and they hit the ball up."
The game was still reachable at 7-4 going into the top of the ninth, but the inning unraveled after Logan hit Reed Johnson with one out. Christian Yelich and Garrett Jones also walked before Giancarlo Stanton, who doubled in a run in the third inning, delivered a two-run single.
Nicasio would give up a McGehee single to load the bases before Ozuna sent a 2-2 fastball over the left-field wall.
In the bottom of the ninth, Brandon Barnes tripled for his Majors-leading 15th pinch-hit (his three pinch-hit triples also lead the Majors), and he scored on Charlie Blackmon's single, but the deficit was too large.
"We stayed in the game where we needed to be, and the lead got out of hand," Dickerson said.