Hudson had a career-high 12 strikeouts and took a six-hit shutout into the ninth before the ball began to bounce the Marlins' way.
"When you get lucky, you win games," said Alfredo Amezaga, whose flared single tied the score.
"I feel bad for Hudson that he doesn't win the game," Olivo said. "But that's baseball."
Hudson gave up singles to the first three batters in the ninth, then departed after throwing 112 pitches. His ERA, a major league-best 0.62 ERA to start the game, nearly doubled to 1.22.
"For me, it's the most disappointing loss of the season for us," Hudson said. "I felt as good as I have all year. But it stings that we didn't win the ballgame."
Olivo doubled home Florida's first two runs. With one out and the bases loaded, he scored without a play when a sinking fastball eluded catcher Brian McCann.
"I just dropped it," McCann said. "I'm not going to make any excuses. I have to catch it."
The unearned run was the first run off Wickman this season, and the blown save was his first in seven chances.
"All I had to do was get three outs before they scored three runs," Wickman said.
Instead, Florida took the series 2-1, and the Braves lost for the 12th time in their past 17 games in Miami.
"It was only three runs early," Olsen said. "A lot can happen."
It did -- but not until the ninth.
"We got dominated for absolutely two hours," Florida's Aaron Boone said, "and then win in the last 15 or 20 minutes."
"Three straight groundballs in the ninth -- not one was close to anyone," Braves manager Bobby Cox said. "It was the most amazing thing."
Wickman (1-1) came on, and Olivo lined his first pitch for a two-run double. Joe Borchard was intentionally walked to reload the bases.
"The Amezaga at-bat killed us," Hudson said. "Wicky couldn't have made a better pitch, and he hit it about 80 feet for a hit."
With the count 1-1 to Dan Uggla, McCann failed to handle Wickman's pitch, and the ball went to the backstop. Olivo slid home, and the Marlins erupted in celebration.
The stunning turnaround prevented Hudson from improving to 4-0.
"We kept saying, `We're going to get him. We're going to get him,"' Ross said. "It was a little later than I anticipated."
Ross conceded the Marlins stole one.
"As good as Hudson was, I'll take a steal," Ross said.
Rookie Henry Owens (1-0) pitched a 1-2-3 ninth for his first major league win.
The Braves began the game tied for NL lead 26 homers, and their first three batters hit the ball nearly 1,200 feet. Johnson led off with his fifth home run, Edgar Renteria flied out to the warning track, and Jones hit his seventh homer. Diaz ended an 0-for-17 skid with his second homer in the second.
But Atlanta was shut out on five hits over the final 7 2/3 innings.
In an attempt to change the Marlins' fortunes against Hudson, manager Fredi Gonzalez shook up the lineup, batting Hanley Ramirez third for the first time in his career. But Ramirez went 0-for-4 with two strikeouts, ending his 11-game hitting streak.
- Atlanta's Andruw Jones struck out three times and left the bases loaded in the fifth. He went 0-for-4 and is 0-for-14 against Olsen with seven strikeouts.
- Borchard ended a 3-for-26 stretch with his double.
- Olsen's average fell to .556 (5-for-9).