One ball scooted under the glove of shortstop Jamey Carroll. Another sailed over the glove of left fielder Jerry Sands.
"I just whiffed it," Carroll said after the Dodgers let victory slip away. They wasted a strong start by Jon Garland and a major league record-tying single by Andre Ethier, who extended his hitting streak to 22 games, matching the longest ever in April.
"Two-out walks will kill you every time," Broxton said.
Pinch-hitter Hanley Ramirez, held out of the starting lineup because of a 2-for-27 slump, followed with a single to put runners at first and third. Scott Cousins' two-out grounder then rolled under the glove of a charging Carroll for an error, and Bonifacio scored.
"I went hard after it and just missed it," Carroll said. "I don't know if I looked up, but I know I didn't follow it into the glove."
Added Dodgers manager Don Mattingly: "It's probably going to be a tough play, but it is the one guy you really want the ball hit to."
After Chris Coghlan was intentionally walked to load the bases, Omar Infante pulled a 1-0 pitch to left. Sands started in, braked and leaped, and the liner cleared his outstretched glove and fell for a game-ending single.
"I took a step and just tried to get there," Sands said. "It was hit pretty hard, I just tried to make a play on it and it got past me. It was probably a bad jump on my part."
Because of the defensive lapses, Broxton (1-1) blew a save for the first time in seven chances.
The game was the first for the Dodgers under former Texas Rangers president J. Thomas Schieffer, who was hired by Commissioner Bud Selig to run the team less than a week after Major League Baseball took over operation of the franchise from owner Frank McCourt.
Coghlan hit two solo homers for the only runs off Garland, who went seven innings. Garland allowed four hits and one walk.
"Taking the team seven innings, and an opportunity to win the game — that's what I'm trying to do every time out," Garland said.
Ethier singled in the first to extend his hitting streak. It equaled the mark set by his former manager, Joe Torre, who hit in 22 consecutive April games in 1972.
The Dodgers scored their first run in the fourth on Sands' two-out RBI single. Sands, who came into the game with four hits this season and a .154 average, finished 3 for 4.
Teammate Matt Kemp went 1 for 4, dropping his average from a major league-leading .402 to .396.
Florida's Brian Sanches (3-0) extended his scoreless streak to start the season to 13 2-3 innings with a perfect ninth.
The Marlins earned their ninth comeback win and improved to 5-1 in one-run games. They're 14-7 overall to match the best start in franchise history, achieved in 2004, and they're 6-1 on their homestand.
They're winning even though their star shortstop hasn't been hitting. Ramirez declared his slump over after the single hiked his average to .194.
"It gives me a lot of confidence," he said. "I feel so much better right now. I'm where I want to be right now."
Notes: Marlins LF Logan Morrison (left foot) had a cast removed and said he felt no pain. He hopes to be activated as soon as he's eligible to come off the disabled list May 5. ... Dodgers 3B Casey Blake (groin) was held out. INF Juan Uribe (thigh) missed his third game in a row but is expected back Tuesday. ... The Marlins turned a double play in the second when Sands tried to steal second. Rod Barajas struck out, and when he was called for interfering with the catcher's throw, Sands was also out. ... Stanton broke his bat in the sixth when he grounded to third baseman Miles, who deftly avoided the flying barrel to scoop up the ball and make the throw to first.