"We just needed to win a series," Marlins manager Mike Redmond said. "We've come out strong that first game for whatever reason and to win a series against a great team and a team that we've had really some great battles against all year (is great)."
Teheran (13-11) allowed four runs and eight hits in 5 1/3 innings.
"Teheran is a great pitcher. He doesn't give up very many runs, so we got that one and I just wanted to go out there and keep the lead," Hand said.
In a tight race for the second NL wild card, the Braves have lost four of five. Atlanta was shut out for the fourth time in its last eight games.
"Teheran just gave up four runs and on most nights he's got a chance to win that game," Braves manager Fredi Gonzalez said.
Teheran set down 13 in a row before Garrett Jones doubled in the fifth. Saltalamacchia followed with an RBI single to left field, giving Miami a 1-0 lead.
"It looked like early that that was going to be a real pitchers' battle. Especially a day game, it looked like there were some tired guys out there," Redmond said.
But then the Marlins were able to get to Teheran, who entered 4-0 with a 2.31 ERA in seven starts against Miami. He allowed four hits in the sixth, including an RBI single by Solano and an RBI double by Ozuna. The right-hander exited with the Braves trailing 3-0.
"I think they made adjustments on the way I was pitching today," Teheran said. "I think later on in the game they were right on my fastball; they were chasing my fastball really good."
Saltalamacchia added a sacrifice fly.
Marlins: RHP Henderson Alvarez (left oblique strain) threw a bullpen before the game and did not feel any discomfort. The team hopes he can rejoin the rotation this week.
HAND AT HOME
Hand is 2-2 with a 2.67 ERA in his last four home starts. He is 1-2 with a 5.16 ERA in his last four road starts.
ANGRY YOUNG MAN
Teheran slammed down his glove in the dugout after he was pulled.
"He competes," Gonzalez said. "He doesn't want to come out of games and I don't blame him. I don't want anybody to come out of games. He's got to keep pitching the way he pitches and hopefully we can start swinging the bats."