Eric Young Jr. and Josh Rutledge had a hit and an RBI apiece for the Rockies, who won their fourth straight game.
Rafael Betancourt tossed a perfect ninth for his 22nd save. Colorado is perfect on this current seven-game homestand after going 1-8 at Coors Field two weeks ago.
"Winning cures a lot," Cuddyer said.
Nolasco (9-12) lost for the sixth time in his past seven starts despite going the distance. He allowed five runs and nine hits, struck out seven, and walked one in eight innings.
"Overall, Nolasco pitched well," Marlins manager Ozzie Guillen said. "We didn't score enough runs."
Six of Nolasco's strikeouts came in the first 3 1/3 innings, before the Rockies made an adjustment that helped them rally late.
"We wanted to get him up in the zone, force him to throw strikes," Young said. "Balls we were swinging at weren't strikes. That's why he was able to go deep into the game."
The Rockies got to Nolasco in the sixth. Carlos Gonzalez reached on a one-out bunt single to bring up Cuddyer.
Cuddyer had struck out on balls in the dirt in his first two at-bats. This time he crushed Nolasco's 82 mph slider into the left-field seats to erase a 3-1 deficit in the sixth. It was his 16th homer of the season.
"If you swing at enough of them, he'll hang one," Cuddyer said. "The ones I struck out on were in the dirt. This one wasn't."
Colorado then went ahead in the seventh.
LeMahieu led off with a single and scored on a triple to right by pinch hitter Rutledge. Young came to the plate guessing manager Jim Tracy would have him lay down a squeeze with the speedy Rutledge on third.
"I knew walking to the plate that Tracy would probably put it on," Young said. "They say try to think along with the manager. I was all for it. Just kind of go to who hates fielding bunts the most."
Young put down a squeeze bunt to Lee up the first-base line to knock in Rutledge and give the Rockies a 5-3 lead.
"I had (Rutledge) 0-2 and couldn't make a pitch, and you saw what happened," Nolasco said. "You make good pitches all night and then make a couple of mistakes, and that's the game. I left that ball up to Cuddyer. He's such a good hitter. He got the important hit to tie the (game), and things got out of control in the seventh inning."
The Marlins scored first on Lee's leadoff homer in the second inning, his seventh of the season. The Rockies tied it in the bottom half when LeMahieu tripled with two outs and scored on a wild pitch.
Miami went back ahead in the fourth when Lee walked, went to third on Greg Dobbs' single and scored on a wild pitch.
Stanton made it 3-1 with a leadoff homer off Ottavino in the sixth. It was his 22nd of the season.
"Ottavino did a tremendous job of settling the waters," Tracy said. "His only mistake was the pitch to Stanton."
The Rockies optioned Matt McBride to Triple-A Colorado Springs to make room for Cuddyer on the roster. ... Marlins C Rob Brantly's double in the sixth was his first major league hit. ... Rockies RHP Jhoulys Chacin (pectoral injury) was scheduled to start for Colorado Springs on Thursday and could join the team when it travels to New York on Monday. ... Miami LHP Wade LeBlanc (1-2) will face Colorado's Jeff Francis (4-4) on Friday.