Miami had season highs in runs, hits (17) and extra-base hits (10).
"It feels good," said Brinson, who has nine home runs in a rookie season filled with inconsistencies thus far. "We got the win, on top of a great night by pretty much everyone in the lineup. I think everybody had a hit. We had a great night. It's good to see some of the work paying off a little bit. But we came out ready to play. We put it on a really good team. I'm glad we got the win like that."
Regarded as one of the young building blocks of the organization, Brinson entered the night batting .161, including going 4-for-22 in the first eight games of the road trip.
Brinson got his three-hit night going with a single off a Jack Flaherty breaking ball in the second inning. He homered in the seventh off Preston Guilmet, and in the ninth inning, with the game out of reach, Brinson went deep off infielder Jedd Gyorko, who started the game at second base.
The second-inning single helped Brinson get locked in for the night.
"That's something you know is in there," said catcher J.T. Realmuto, who had two doubles and a triple and was hit twice by pitches. "You watch him take BP, and you see he's got crazy power. It's something that eventually, once he hones in and works on his approach, he's going to be an unbelievable hitter for average, and also have that pop, so he's definitely getting better every day, and you can see it."
After scoring a total of four runs in three losses last weekend at Arizona, the Marlins have taken the first two games, clinching the three-game series at St. Louis.
Dietrich, who drove in three runs, had a career-high four hits. Brinson added three hits, including his second multi-homer game. Starlin Castro delivered three doubles and a single, scoring three times. Brian Anderson chipped in with a double and two RBIs.
"There were great at-bats up and down the lineup, one through nine," Realmuto said. "You even had a pitcher hit the ball hard there at the end. It was good run production up and down the lineup, which is huge for us."
The Marlins entered Wednesday last in the Majors in runs (203), home runs (45) and slugging percentage (.349). Miami then got to Flaherty, who threw five innings and allowed six runs (four earned) on eight hits.
Marlins starter Wei-Yin Chen went only 4 1/3 innings, getting lifted after 91 pitches with the Marlins leading, 6-2. Drew Rucinski stranded two runners in relief of Chen in the fifth inning, going on to earn the win.
"I think the team did great," Chen said through an interpreter. "Dietrich and Castro hit really well tonight and gave me a lot of run support. It's just unfortunate I couldn't finish five innings and get the win."
MOMENTS THAT MATTERED Rucinski escapes jam: The Marlins scored three runs in the fifth to take a 6-2 lead, putting Chen in position to qualify for a win, if he could make it through the fifth. But after a one-out single by Tommy Pham and a walk to Jose Martinez, manager Don Mattingly went to the bullpen, calling upon Rucinski, who induced a fielder's choice grounder from Marcell Ozuna before striking out Yadier Molina.
Rucinski worked 2 1/3 innings, allowing one run and logging his first big league win.
YOU GOTTA SEE THIS Brinson's home run off Gyorko, a position player, in the ninth inning, was projected by Statcast™ at 412 feet, with an exit velocity of 101 mph. The pitch by Gyorko came in at 73.4 mph.
"I hate facing position players," Brinson said. "In the Minor Leagues, I'd face them sometimes and either strike out or pop up. It gets in my head too much. I'm glad I was able to put a pretty good swing on it."
HE SAID IT "I think it helped a lot. Guys were ready for that off-day. Long road trip against two tough teams, going cross country. A lot of factors in there. You don't want to make excuses. I think that off-day, coming off those two tough series, really helped us out, getting ready for this series against a really tough team." -- Brinson, on Monday's off-day following six straight losses at San Diego and Arizona
UP NEXT The Marlins are calling up rookie Trevor Richards from Triple-A New Orleans to join the rotation. The right-hander will start the series finale at Busch Stadium at 1:15 p.m. ET. Richards was last with the Marlins on April 25, when he struck out 10 in 4 2/3 scoreless innings. He has made five starts for Miami this season. Miles Mikolas is starting for the Cardinals.