Along with belting a club-record 12 home runs in the month, Stanton has driven in a franchise-best 30 runs after his RBI single and home run against the Nationals on Wednesday.
In Miami's last game of the month, Stanton belted a homer and drove in two runs, capping one of the best overall months in team history.
Stanton connected on a home run off Washington's Ryan Perry in the seventh inning on Wednesday.
Miguel Cabrera had 30 RBIs in 2006. Stanton had previously passed Preston Wilson, who had 27 in 2000.
"It's a tribute to the guys ahead of you getting on base," said Wilson, now a pregame and postgame analyst for the Marlins on Fox Sports Florida. "It's also a tribute to when you get a home run, there are not many solo home runs. When you have a month like that, when you hit a home run, it's either a two-run or three-run homer.
"When you get guys on and you capitalize on those situations, you have a great month like that."
Stanton now shares the homer mark with Dan Uggla, who hit 12 in May 2008. Uggla drove in 26 runs that month.
The Marlins record for RBIs in any month is 33, by Hanley Ramirez in June 2009. And Cabrera had 32 in August 2006.
The May Stanton is having should make him a strong contender for National League Player of the Month.
"I don't follow who's hot or who's not," manager Ozzie Guillen said. "I doubt many have put up better numbers than him this month. Maybe somebody out there. I don't know which one. Whoever had better numbers this month better than [Stanton], he had a very good month."