Beachy, making his third start since coming back from major elbow surgery, won for the first time in nearly 15 months.
As for his team, the Braves are surging and have won 14 straight games to seemingly take all the suspense out of the NL East race.
"It makes pitching a little easier when those guys work their tails off and put five (runs) up there for me early," Beachy said. "I don't have to be fine. I can go right at guys, and I tip my cap to them. Glad they're on my team."
The Braves are one victory shy of tying their 2000 team for the longest winning streak since the franchise relocated to Atlanta in 1966.
Beachy (1-0) scattered three hits, allowed one walk and struck out six in eight innings to win his third start back from elbow ligament replacement surgery on June 21, 2012. He made 67 of 99 pitches for strikes.
With only 15 losses at Turner Field, Atlanta improved its home winning percentage to .722, best in the majors.
The Braves were eight games ahead of second-place Washington in the NL East after losing their last game, July 24 at the New York, but now lead the division by 15 1/2 games.
"We want to keep getting better every single day we come to the park and try to keep our foot on the gas as best we can," Johnson said. "We want to be playing good baseball going into the end of the season and into the postseason."
The Marlins began the game having lost five straight by a total of seven runs, but their sixth consecutive loss unraveled early as Atlanta took a 4-0 lead in the first on Upton's 22nd homer and Johnson's three-run shot.
After Johnson hit his eighth homer, Marlins starter Jacob Turner hit Dan Uggla in the upper left arm with a pitch, and Uggla yelled at the pitcher and catcher Jeff Mathis as he walked up the first-base line.
Home plate umpire Mike Estabrook issued a warning to both dugouts before Turner faced the next batter, and the game ended without another incident.
"I would never try to throw at someone's head like that, and I told him," Turner said. "I think it (Uggla's reaction) was just one of those in the heat of the moment."
McCann led off the third with his 17th homer to make it 5-0.
Turner (3-4) allowed five hits and five runs -- four earned -- with three walks and five strikeouts in five innings. The right-hander dropped to 0-7 with a 3.71 ERA in 11 career road starts.
Beachy, who had gone seven straight starts without a win, allowed a leadoff single to Christian Yelich in the first, but retired the next 11 batters he faced before Logan Morrison's leadoff single in the fifth.
The right-hander snapped a seven-start winless streak, earning a victory for the first time since pitching his first career shutout in a 7-0 victory over Miami on May 17, 2012. At the time of his injury one month later, Beachy had a 2.00 ERA that was tied for the major league lead.
"I still have a lot of room for improvement with the curveball and especially the slider," Beachy said. "Fortunately I was able to command the (fastball and change-up) well enough to where I can get by and continue to work on the others and hopefully piece it all together, little by little, each start."
Miami's third hit was a one-out double by pinch-hitter Juan Pierre in the sixth, but Beachy fielded a grounder from the next batter, Yelich, and threw Pierre out at third.
Johnson, who leads the NL with a .338 average, went 1 for 4. Over his last 40 games, the Braves' third baseman is hitting .367.
Upton has six homers and 13 RBIs in his last eight games. He loves how Atlanta keeps putting pressure on opposing pitchers.
"He's got to make his pitches and knowing the next guy coming up is pretty dangerous, too," Upton said. "There are no holes to give that pitcher a break. I think that wears of them and allows us to settle in and get good pitches."
Dan Jennings relieved Lucas to begin the sixth and allowed two hits over the next two innings.
Scott Downs began the ninth for Atlanta, allowing a leadoff single to pinch-hitter Koyie Hill and striking out Yelich before Luis Ayala needed two pitches to end it on Jake Marisnick's double-play groundout.
Braves RHP Tim Hudson said before the game that he hopes to return from full health from ankle surgery and play his 15th season in 2014. The 38-year-old Hudson added that he wants to return for a 10th year with Atlanta. ... Rob Brantly, the Marlins' opening day catcher, was optioned to Triple-A New Orleans earlier in the day. Hill had his contract purchased from New Orleans to take Brantly's spot on the 25-man roster. Brantly hit .225 with one homer and 18 RBIs in 59 games and allowed seven passed balls. ... The Braves announced that OF Jordan Schafer will be activated from the 15-day disabled list on Saturday and OF Jose Constanza will be optioned to Triple-A Gwinnett.