"Maybe the farthest. I don't know about the hardest," Stanton said when asked how his 462-foot shot compared to the other eight homers he's hit this season. "But that was pretty good."
Austin Kearns tied a career-best with four hits for the Marlins, whose 15-5 record in May leads the majors.
Buehrle (4-4) worked 7 2/3 innings, giving up four runs and four hits in the first and one more hit the rest of the way.
"When you talk about bulldog, when you talk about gamer, there's a lot of fake out there," Marlins manager Ozzie Guillen said of Buehrle. "There's a lot of fake bulldogs. This kid's for real."
Moyer (2-4) allowed nine hits and six runs in 3 2/3 innings in his debut at Marlins Park, the 50th big-league stadium in which the 49-year-old has appeared during his career.
"It's hard to win when you get 3 2/3 from your starter and over 100 pitches," Rockies manager Jim Tracy said. "We get four hits and four runs with the first five hitters in the game and we get one hit and two walks from the second inning on."
Stanton wasn't even born when Moyer's career began in 1986. His first game against him was one to remember.
Miami's big fourth got going with one out, when Buehrle hit a soft double -- the second of his career. He scored when Jose Reyes' single was bobbled by center fielder Dexter Fowler. Moyer nearly escaped further trouble, but walked Hanley Ramirez on a full count with two out, then walked Kearns to load the bases.
That brought up Stanton, who watched Moyer's 2-2 offering just miss -- replays showed the inside pitch wasn't out of the zone by much, if at all.
"I kind of backed myself into a corner -- walks, a lot of pitches, deep in the count," Moyer said. "It's not the way to be an efficient pitcher. Ultimately, I got what I deserved."
Moyer's next pitch was 72 mph. It went out faster.
Stanton's ninth home run of the season and fourth career grand slam went down the left field line, the impact of its collision with the videoboard over the left-field concourse temporarily knocking out a portion of the digital display. The Marlins had a 6-4 lead, and the crowd roared for nearly a minute before Stanton acknowledged their desire for a curtain call.
"I looked it up and 1986 was his debut and I wasn't even a thought at that moment," Stanton said of facing Moyer. "I was born three years later."
Meanwhile, Buehrle was in a groove.
Buehrle got hit hard in the first, literally and figuratively. Jordan Pacheco lined a ball off Buehrle with one out, and scored along with Carlos Gonzalez two batters later when Cuddyer's double beat Kearns to the left-field wall. Tulowitzki followed with a homer to left that put the Rockies up 4-0 before Moyer even saw the mound.
Buehrle didn't give up another hit until Pacheco's two-out single in the eighth, tipping his cap to the crowd as he departed. Heath Bell pitched the ninth for his sixth save in 10 chances for Miami.
"The first inning, I thought it was going to be a long night," Buehrle said.
Moyer has pitched in more ballparks than anyone since at least 1921, and was 8-2 in the Marlins' former home, Sun Life Stadium. Guillen -- one of 11 current managers to bat against Moyer in their careers -- went 4 for 22 against the lefty, and several members of the Miami coaching staff and front office also have faced him at one time or another.
"I don't remember much," Guillen said about his times against Moyer. "I know he went from very bad to very good to very old. ... I feel proud to know him.
Miami added an insurance run in the seventh, when Ramirez tripled and scored on Kearns' fourth hit.
Stanton is the eighth player to hit a grand slam off Moyer, and Buehrle had never before batted twice in an inning until the fourth, according to STATS LLC. ... Miami RHP Ricky Nolasco (4-2, 4.10) is the Marlins' scheduled Tuesday starter against Colorado's Juan Nicasio (2-1, 4.37). ... Kearns stole second in the third inning, his first time swiping a bag since June 6, 2010. ... The Marlins hope to have 2B Omar Infante back Tuesday. Infante left the team Sunday to attend a family funeral in Venezuela. ... Pacheco extended his hitting streak to seven games.
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