Brantly scored in the eighth inning, Solano followed with a homer as part of a four-run ninth, and the Marlins overcame a 93-minute rain delay to beat the Rockies 5-3 on Thursday.
"We put that five-spot up, they came back, we were able to hang on for the win," Marlins manager Mike Redmond said. "Great job to salvage what looked like was going to be a real rough road trip, and to win three games here in Colorado, a tough place to win."
Miami finished its seven-game trip by taking 3 of 4 from the Rockies after getting swept at Milwaukee. It was the Marlins' first series win at Colorado since 2009, when they took 2 of 3.
"All the years I've been coming here, those are the kind of games you play," said Redmond, who played 13 years in the majors. "You score two or three or four and then give up two or three. They mounted a rally. That's what happens here."
The Rockies were also stung by the loss of slugger Carlos Gonzalez after the third inning when he aggravated a sprain of the middle finger on his right hand. The team said he is day to day.
Gonzalez has been dealing with the injury since July 7 when he initially sprained his finger during an at bat against Arizona. He aggravated it striking out swinging in the first inning and was replaced by pinch-hitter Jordan Pacheco.
Reliever Adam Ottavino (0-2) struck out the first two batters he faced in the eighth before Brantly singled to right. Greg Dobbs, batting for reliever Dan Jennings (1-1), singled him to third. With Adeiny Hechavarria at the plate, Ottavino uncorked a pitch that bounced in the dirt and shot past catcher Wilin Rosario, allowing Brantly to score.
"We were just playing no doubles, and those two balls found a hole," Ottavino said. "I spiked a pitch. It got away and that's it. That's how quick it can happen. I thought I threw the ball all right, but nothing went my way. Nothing went the team's way today."
Rosario said he was late in his attempt to slide to his right and stop the pitch.
"I've got to block that ball," he said. "That's my responsibility. Maybe if that run doesn't score, we come back in the next inning. I didn't react in time."
In the ninth, Giancarlo Stanton had an RBI double, and Ed Lucas added an RBI single off Wilton Lopez before Solano drove the first pitch he saw into the left field seats for his second homer of the season.
"I was waiting for that pitch, a little bit in, and tried to elevate it," Solano said. "I got a good swing on it, and that's it. Hit a home run."
The Rockies rallied off Kevin Slowey for three runs in the ninth. Steve Cishek relieved, and after yielding a one-out single to Nolan Arenado, he induced Jonathan Herrera to ground into a game-ending double play for his 20th save in 22 chances.
Miami starter Nate Eovaldi threw six scoreless innings, and Colorado's Juan Nicasio had a season-high nine strikeouts in seven scoreless innings. Neither pitcher returned after the delay caused by wind-driven thunder showers in the middle of the seventh.
Jennings pitched a scoreless seventh to earn the win.
Marlins OF Marcell Ozuna will have season-ending surgery on Friday to repair torn ligaments and an avulsion fracture of his left thumb. He was playing center field at Colorado on Monday when he was injured making a diving catch on a sixth-inning drive by Michael Cuddyer. ... Stanton went 2 for 4 with a pair of doubles, an RBI and one run scored. He's batting .333 with four doubles, 7 home runs and 13 RBIs in 11 career games at Coors Field. ... The Marlins return to Miami to open a 10-game homestand starting Friday against Pittsburgh, with Henderson Alvarez (0-1) slated to pitch the opener against the Pirates' Jeff Locke (9-2). ... Colorado continues its homestand by opening a three-game set against Milwaukee. The Rockies' Tyler Chatwood (6-3) facing Wily Peralta (7-9). ... Nicasio's nine strikeouts were one below his career high.