With that, the Phils waltzed back to Philadelphia riding their longest winning streak in three years.
Happ (7-0) escaped a bases-loaded, none-out jam in the sixth to help the Phils win for the 12th time in the past 13 games. The winning streak is their longest since taking nine in a row April 30-May 9, 2006.
"We have a lot of confidence, and I have a lot of confidence in the guys," Happ said. "It makes it fun to have them go out there behind me."
Happ helped himself with a two-out single to start a three-run rally in the second inning. Rollins had three hits by the third and came within a home run of the cycle, while Raul Ibanez doubled home two runs to help the Phillies complete their second three-game sweep in Miami this season.
Florida fell seven games behind the Phils in the NL East.
"If they keep going the way they've been going, it's going to be tough to catch them, no matter what we do," Marlins outfielder Jeremy Hermida said.
Florida, which began the series in second place, slipped below .500.
"We dug ourselves a little hole -- a big hole," Marlins manager Fredi Gonzalez said.
The Phils improved to 29-15 on the road, best in the majors. They're especially tough in Miami, where they have won eight in a row since last year while outscoring the Marlins 49-18.
Happ's on a roll, too. Even when the Marlins loaded the bases with none out in the sixth on two singles and an error, he escaped by retiring the next three batters, two on strikeouts.
"That right there is how you learn to be a good pitcher," Phillies manager Charlie Manuel said. "When he gets in a jam like that, it's good for him. When he gets out, it shows he keeps his composure."
Happ, who leads NL rookies in wins, pitched at least seven innings for the fifth start in a row. He allowed five hits and lowered his ERA to 2.68.
The left-hander has been mentioned in recent trade speculation, including buzz about a blockbuster deal that would bring Toronto's Roy Halladay to Philadelphia.
"I like pitching here," Happ said. "I want to be known as a guy they can count on, and that's what I'm trying to work toward."
When asked about trade rumors involving Happ, Manuel said: "He's doing a tremendous job. We want the best rotation we possibly can get, and he's definitely part of that."
For Florida, Andrew Miller (3-5) lasted only 2 2/3 innings for the second game in a row. He allowed six hits, four walks and four runs, and he fell to 0-3 in six career starts against the Phils.
Rollins came into the game 1 for 15 against Miller, but by the third inning he had a single, double and triple. Rollins struck out in the fifth and hit into a double play in the eighth.
The 2007 National League MVP has struggled this year, but he's batting .353 during the winning streak to hike his average to .236.
"When he gets on base, he makes things happen and it's definitely a different offense," Ibanez said. "He's such an electric player."
Miller gave up three runs in the second after retiring the first two batters. Happ reached on an infield single, Rollins singled and Shane Victorino loaded the bases with an infield single. Chase Utley fell behind 0-2 but was hit by a pitch to force in a run, and Ibanez doubled to make it 3-0.
Rollins doubled home a run in the third to end Miller's afternoon.
Manuel said RHP Pedro Martinez will probably pitch at least twice in the minors before joining the Phillies. Martinez's first start will be for Class-A Clearwater, and he may pitch at least one game for a higher-level affiliate, Manuel said. ... Between innings, former Marlins manager Jack McKeon unveiled a sign on the left field wall counting down the home games until the opening of the team's new ballpark. The number Sunday stood at 194. ... Phils 1B Ryan Howard, who is 1 for 12 against Miller, was held out of the starting lineup. ... RHP Rodrigo Lopez, scheduled to start Monday for the Phillies against the Cubs, allowed eight earned runs in 4 2/3 innings the only other time he faced Chicago two years ago.