A crowd of 16,493 fans at Marlins Park watched Turner provide a spark in his first big league start of the season.
Miami's struggling offense had a couple of unlikely heroes in Ed Lucas and Jordan Brown.
Lucas collected his first big league hit, which was the go-ahead RBI single in the seventh inning. Also in the inning, Brown added a pinch-hit two-run double, and the Marlins were able to celebrate their first win since beating the Phillies, also 5-1, on May 20.
"When you need a big win, you need guys to step up," Marlins manager Mike Redmond said. "We talked about that last night, who was going to be the guys to step up."
Lucas started at shortstop to give Adeiny Hechavarria a night off.
"Lucas goes out there, he makes his Major League first start of his career and gets a big hit," Redmond said. "He did his part to help us win. Brownie comes off the bench -- big hit, huge hit, great at-bat."
Turner, Lucas and Brown all came through on Friday night. Just a few weeks ago, they were all teammates at New Orleans.
"That's what we're talking about," Redmond said. "It doesn't matter who it is to help us win. You just need somebody to step up and get the big hit or get the big out."
In a season filled with disappointments and injuries, the Marlins are relying on a number of players who entered the season as prospects.
Rookie Marcell Ozuna, who started the season at Double-A Jacksonville, had three hits and an RBI, extending his hitting streak to 16 games -- the longest active in the Majors. It's also the second-best stretch by a Marlins rookie, topped only by Edgar Renteria's mark of 22, set in 1996.
Lucas, Ozuna and Brown gave a boost to the lineup, but it was the pitching of Turner that set the tone.
"This is the best we've seen him, I can tell you," Mets manager Terry Collins said. "We saw him last year, and his command was much, much better from the last time we saw him. He moved the ball to both sides of the plate, got his slider over for strikes. He did a nice job."
Entering Spring Training, Turner was projected to be in the Marlins' rotation. But the 22-year-old struggled in camp, and opened the season at New Orleans, where he settled into a nice groove in May.
After posting a 6.56 ERA in five April starts, Turner's next five were considerably better. For the Zephyrs in May, he posted a 3.00 ERA in 33 innings, earning Miami's rotation spot vacated when Alex Sanabia went on the disabled list with a right groin strain.
"Obviously, it was a good start, and I'm glad we got the win," Turner said. "I feel like I've been throwing the ball similar to this in Triple-A. It was just a matter of time to make the adjustments I needed to make to get everything right.
"My last five or six starts, everything has been coming together. Obviously, it took a little bit longer than I would have liked. I'm happy that it's here now."
After scoring three unearned runs in their two straight losses to the Rays at Marlins Park, the Marlins on Friday were able to push across four runs, all earned, in the seventh inning off Mets right-hander Shaun Marcum to gain momentum.
Derek Dietrich doubled to start the rally, and he moved to third on Ozuna's flare single to right-center. With one out, Lucas floated an RBI single to right-center.
Lucas, a 31-year-old who spent 10 years in the Minor Leagues before his callup, wondered if he would ever get a chance to notch his first big league hit.
"Definitely," Lucas said. "It's been 10 years, and that's entered my mind plenty of times. But I never stopped hoping, and I finally got an opportunity. I was really glad I was able to fit that one in. Hopefully, there are more to come."
Jeff Mathis added a sacrifice fly to center, and Brown laced a two-run double to left-center, giving Miami some breathing room.
"Any time my name is called, especially lately, with runners on base, my only thought is, 'Just stick one in the gap,'" Brown said. "Get a pitch up in the zone and stick one in the gap. If I think of anything other than that, I'm an easy out."
The way Turner pitched, the Marlins didn't need much run support.
"He's motivated," Redmond said. "He didn't want to start the year in Triple-A, and why would you? Everyone should play this game with a little bit of a chip on their shoulder. That makes you a better player. He went out there tonight to prove something, and he did that.
"He went out there, he pounded the strike zone, he showed that he belonged here. Hopefully, he can build off this and continue to go out there and give us some solid innings."