"This guy is a huge part of our team," Marlins manager Mike Redmond said of Ozuna, who snapped an 0-for-16 skid earlier in the game. "And he's had some big at-bats and he's gotten some big hits for us throughout the year."
Ozuna's line-drive to left-center came off Bradin Hagens (0-1), who was making his major league debut. Hagens got a double play to escape the ninth, but Jones reached on a leadoff walk in the 10th and scored two batters later.
"I still have to be ready," Hagens said. "It was nice to get in and have a chance to help the team get a win, just unfortunate that it didn't happen."
Mike Dunn (10-5) pitched two perfect innings for Miami and became the first reliever to reach double-digits in wins since Matt Belisle for Colorado in 2011, according to STATS.
"The team played great tonight, coming back," Dunn said.
Mark Trumbo had a pair of RBI singles for Arizona. Diamondbacks starter Chase Anderson allowed nine hits and three runs in six innings, and David Peralta had an RBI triple to highlight a two-run third.
Giancarlo Stanton had three hits for Miami, giving him four multi-hit games in his last 10 outings. Brad Penny, pitching at home for the Marlins for the first time in more than 10 years, allowed five hits and four runs in five-plus innings.
Miami trailed 3-0 early, then chipped away.
Penny and Donovan Solano had doubles in the home half of the third, and Stanton's RBI single got Miami within 3-2. Arizona went up 4-2 in the sixth when Trumbo drew a leadoff walk and eventually scored, but then Hechavarria -- who had exactly one multi-RBI game in his last 108 appearances before Thursday -- brought the Marlins back.
He had a RBI triple in the sixth to get the Marlins within one, then tied it at 4-4 with two out in the eighth with a single that brought home pinch-runner Jordany Valdespin easily from second.
"He's improved so much," Redmond said.
Penny's most recent home start for the Marlins was July 28, 2004 -- which wasn't even in Miami, but rather about 15 miles north in Miami Gardens, Florida at Sun Life Stadium, the facility where the team played before its Little Havana ballpark was built.
Diamondbacks: 2B Aaron Hill was out of the lineup for the second straight game, with manager Kirk Gibson saying he was "pretty beat up" but not citing any specific injury. LHP Eury De La Rosa and RHP Randall Delgado were not available Thursday in order to get some rest.
Marlins: LHP Dan Jennings (concussion) is planning on throwing bullpen sessions the next couple of days and is expected to pitch for Single-A Jupiter when the Marlins begin their road trip on Aug. 22. "I'm very pleased with how far he's come in the last few days," Redmond said. Also, INF Derek Dietrich (right wrist) is expected to begin a rehab assignment with Single-A Jupiter on Saturday.
Diamondbacks: RHP Trevor Cahill (2-8, 4.86) has won one of his nine starts this season -- but that win was in his last outing, a 14-4 victory over Colorado on Aug. 9. Cahill is 1-1 in four appearances against the Marlins.
Marlins: LHP Brad Hand (2-4, 4.65) makes his 11th start of the season. He's 0-1 with a 2.38 ERA in two career starts against the Diamondbacks
Arizona came into the night tied with the Los Angeles Dodgers for the major-league lead with 33 triples, and hit two more on Thursday.
Penny gave up two leadoff walks, one of the four-pitch variety to Ender Inciarte to open the game, the other to Trumbo in the sixth. Both runners eventually scored. But he also hit his first double since Sept. 19, 2007 to help get the Marlins' offense going.