Atlanta's loss, combined with Philadelphia's 1-0 win over Milwaukee, cut the Braves' NL East lead over the Phillies to one game.
Morrison became the eighth player to hit multiple triples in a game this season, according to STATS LLC, after hitting only one in his first 126 at-bats. Both came off Atlanta starter Kenshin Kawakami (1-10), who gave up five hits — all for extra bases — five runs and four walks in three innings.
Chad Tracy had two hits and two RBIs for Florida. Miller (1-0) allowed seven hits and one run for his first victory since July 4, 2009, and four relievers combined to finish with four no-hit innings.
The Braves have been alone in first every day since beating Philadelphia on May 31, when they held a half-game lead that eventually ballooned to as much as seven games.
By Saturday night, they may have company.
The Marlins were without manager Edwin Rodriguez, who served a one-game suspension handed down earlier Friday after baseball completed its review of incidents that took place in Florida's game against Washington on Wednesday night.
Florida pitcher Chris Volstad was suspended for six games, pitcher Alex Sanabia for five, first baseman Gaby Sanchez for three. All three Marlins are appealing, and Sanchez drew loud ovations each time he appeared at the plate after clothes-lining Washington's Nyjer Morgan during the melee.
The Marlins landed plenty of hard shots against Kawakami on Friday.
Florida's first six hits all were either doubles or triples, including Morrison's long triples in the first and third innings.
Morrison's first-inning triple to the right field corner scored Cameron Maybin, and then the Marlins' left fielder came home on Hanley Ramirez's double for a 2-0 lead. Kawakami got his first career RBI in the second, cutting Atlanta's deficit in half.
But Morrison struck again in the third, this time going to deep center for his triple, and Tracy followed four batters later with a two-run double that helped Florida extend its lead to 5-1.
Dan Uggla made it 6-1 in the fourth with another RBI double.
NOTES: Atlanta OF Rick Ankiel struck out four times, the third time he's done that in his career. ... Troy Glaus hit a pinch-hit single for the Braves in the fourth inning, his first at-bat since Aug. 17 after a stint on the DL with left knee inflammation. ... Ramirez stole two bases, giving him 30 for the fourth time in his five full major-league seasons. ... The Marlins recalled RHP Chris Leroux and OF Scott Cousins before the game. ... Uggla returned after missing two games with a right groin strain. He made a stellar defensive play in the second, diving to knock down Matt Diaz's chopper, then throwing him out at first.