Stanton's two-run shot off Eric Stults was estimated as the longest home run since the retractable-roof park opened three years ago.
The Marlins entered the game having taking three of four from the Rockies, and they paced the National League with 27 runs scored.
Jumping out quickly on the Padres continued the momentum.
"It was pretty good, especially to start the scoring off," Stanton said. "It was a good punch. This is a new series, a new series. Start over, and get it done."
Adeiny Hechavarria added a career-high four hits, a stolen base and scored two, and Jarrod Saltalamacchia chipped in with a two-run double. Casey McGehee had two RBIs and Garrett Jones and Marcell Ozuna each had one.
McGehee set a Miami milestone by becoming the first player in franchise history to reach 10 RBIs through five games. Stanton is at nine, which is tied for second with Ivan Rodriguez (2003), Alex Gonzalez (2003) and Hanley Ramirez (2009).
Backed by a big lead early, Tom Koehler had the luxury of pitching to contact and letting his defense and the dimensions of the big park work in his favor. The right-hander picked up where he left off after a terrific Spring Training, where he posted a 1.50 ERA.
"When you start a series off with an inning like that, you come out and put a couple of runs on the board early, that's obviously a big relief for Tom Koehler and everybody," manager Mike Redmond said.
In six innings, Koehler allowed two runs on seven hits. He struck out one and walked one. But the walk ended up being costly.
With two outs in the sixth inning, and leading by seven runs, Koehler walked Seth Smith. Yonder Alonso put the Padres on the board with an RBI double, and Jedd Gyorko added a run-scoring single.
By the time Koehler issued runs, Miami was well in control, thanks to a proficient offense.
Brad Hand worked three innings of relief, and picked up his first save since high school. Even though Miami had a big lead, Hand qualified for a save by closing out the game in at least three innings.
Stanton now has two homers to go along with his nine RBIs in five games. A year ago, the slugger got off to a slow start and posted three home runs and nine RBIs in 88 plate appearances in April.
The Marlins estimated Stanton's homer at 458 feet. But according to ESPN Stats, which has its own tracking system, the drive was estimated at 484 feet. The previous distance mark in the three-year-old ballpark was 467 feet, set by Logan Morrison on Sept. 6, 2013.
"He absolutely crushed that ball, but it doesn't surprise me," Koehler said. "I've seen him hit balls further. It's nice to get that lead, and it was a lot better to get back into the dugout faster so they could add back on."
Stanton's drive sailed over the Bud Bar on the concourse, bounced and deflected off a pole. If it didn't hit the pole, it likely would have bounced completely out of the park. When the roof and operable wall are open, like they were Friday, a baseball can literally leave the yard.
Stanton's previous longest drive at Marlins Park was his grand slam off Jamie Moyer in 2012, the shot to left that broke the auxiliary scoreboard. That was estimated at 462 feet.
A year ago, Morrison frequently joked with Stanton when his shot traveled 467.
"Now you can't say LoMo has a bigger bomb than me," Stanton joked. "I thought the one that hit the scoreboard was equivalent. But sweet, that and the scoreboard one."
To adjust to lefty Stults, Redmond gave lefty-hitting Christian Yelich the night off, and went with Hechavarria in the leadoff spot.
In the first inning, Hechavarria had an eight-pitch at-bat that ended with a groundout back to the mound. Jeff Baker got a good look at Stults and singled with one out. Stanton gave Miami an immediate lead with his shot.
The Marlins sent seven to the plate in the third inning and put up three more runs. Hechavarria doubled to open the inning, and Baker walked. Stanton's fly ball out to right moved Hechavarria to third. McGehee lifted a sacrifice fly to right. Saltalamacchia's two-run double gave Miami a five-run lead. He was 3-for-4 on the night.
"For me, the critical at-bat was the Saltalamacchia double on the full-count pitch," Padres manager Bud Black said. "It was a changeup, middle up and that took it from a three-run lead to a five-run lead,"
After tagging Stults for five runs on seven hits in four innings, the Marlins made reliever Donn Roach work in the fifth inning. The right-hander gave up two runs on Jones' RBI double, and Ozuna's fielder's-choice, run-scoring grounder, giving Koehler a seven-run cushion.
The add-on runs are a luxury the team is experiencing now, but didn't occur much last year.
Stanton says those runs are what separates the .260 and .280 hitters.
"If you shut it down, when you are up or down by six or 10, it's a big difference in those last at-bats, when the game doesn't matter, like most people would say," Stanton said.