Gaby Sanchez added his first career home run for the Marlins, who won for the fourth time in five games -- and eighth in 10 -- following a 2-hour, 34-minute rain delay at the game's start.
"It was one of those amazing moments," Sanchez said. "I didn't realize what had happened until I stepped on the plate and got into the dugout."
The victory pulled Florida within five games of Philadelphia in the National League East. The teams are scheduled to play six more times.
"It's fun now, looking at the scoreboard," Cantu said, "but it's up to us to keep winning."
Washington's Justin Maxwell hit two solo homers for his first career multihomer game.
Marco Estrada (0-1) pitched 2 1/3 innings in his first career start. He gave up five runs and three hits, walked three and struck out four.
"I went out there and grabbed some rosin bag that was wet and I had slick hands and for some reason I just couldn't get it off," Estrada said. "I'll learn from it, just don't touch wet rosin bags."
Sanchez allowed two runs, six hits and four walks in 4 2/3 innings.
"Outhitting somebody and losing is not unusual, but losing by eight or nine runs shows how bad we pitched," Nationals manager Jim Riggleman said.
Cantu's three-run homer in the first gave Florida a 3-0 lead.
"Cantu gives you clutch at-bats, and he has 85 RBIs now hitting behind a guy [Ramirez] who's going to have 100," manager Fredi Gonzalez said. "That's not easy."
Washington pulled within 3-1 when Maxwell led off the second with a homer to right. It was his first of the season, and third of his career.
Florida went ahead 5-1 in the third when Cantu doubled home Johnson and Ramirez with one out.
Ross and Gaby Sanchez, as a pinch hitter, homered in the sixth to help the Marlins build an 8-2 lead. Ross led off by lining Logan Kensing's 1-1 pitch over the left-field scoreboard. After Brett Carroll singled, Sanchez lined a 1-1 pitch into the left-field seats.
Ross' run-scoring double and Carroll's sacrifice fly made it 10-2 in the seventh.
Maxwell hit his second homer off Matt Lindstrom with one out in the eighth.
"I just got a couple good pitches and didn't miss them," Maxwell said.
Ramirez's sacrifice fly in the eighth increased Florida's lead to 11-3.
The announced crowd of 38,214 was Florida's third-largest of the season behind 46,427 vs. the Yankees on June 20, and 39,412 vs. the Mets on April 11. ... Washington RF Elijah Dukes (stiff back) was in the original lineup before being replaced by Maxwell. ... Estrada struck out the side looking -- Ramirez, John Baker, Dan Uggla -- in the first. ... Sanchez, who attended the University of Miami, hit his homer on the school's "family night" at the stadium.