The Marlins will have an off day Monday to lick their wounds after playing 17 consecutive days and going 5-12.
"We just played a great team," Redmond said. "We were in every single game and could have won all three. We just weren't good enough this weekend."
The AL West-leading A's, playing in Miami for the first time since 2003, came from behind in all three games. They won their fourth in a row, improved to 7-1 in interleague play and reached the halfway point of 2014 a season-high 21 games above .500 (51-30).
Tommy Milone (6-3) allowed two earned runs in seven innings to win his sixth consecutive decision, a career best. Closer Sean Doolittle was given the day off, and Ryan Cook pitched the final 1 1-3 innings for his first save.
Marcell Ozuna had a pinch-hit drive for his 14th homer, but the Marlins totaled only six hits and hit into three double plays. They had the best home record in the majors earlier this month, but have lost five in a row at Marlins Park.
"We're playing hard, man," catcher Jeff Mathis said. "We're right there. We're in all these ballgames, and even though we're coming up on the short end, we're battling and we're going to keep doing that."
Heaney was nursing a 1-0 lead with two out in the sixth when the AL West leaders made their move. Consecutive singles by Alberto Callaspo, Yoenis Cespedes and Josh Donaldson scored one run, and the 6-foot-8 Freiman pulled a pitch into the nightclub beyond the left-field fence.
A's manager Bob Melvin said Heaney lived up to his reputation.
"We know they are very high on him," Melvin said. "He was on his game, spotting fastballs and throwing just enough breaking balls to keep you off balance. You are just waiting for that one good pitch to hit, and Freiman got it."
Christian Yelich, back in the Marlins' lineup after being sidelined for 15 games by a back injury, made an impact with his first swing. He tripled off the wall to lead off the first inning, and when second baseman Callaspo made an errant relay throw, Yelich scored standing up.
NOTES: The game was halted for 10 minutes in the seventh inning while medical personnel treated two fans struck in the face by the same foul ball. One of them was taken to a hospital for treatment. ... Before the game, the Marlins recalled LHP Dan Jennings from Triple-A. ... RHP Henderson Alvarez (5-3, 2.32) is scheduled to start when the Marlins open a series at home Tuesday against Philadelphia.