Sidney Crosby scored two goals for Pittsburgh, but he and three teammates were denied in the shootout by Kari Lehtonen.
Recchi, claimed off waivers by Atlanta on Dec. 8, also had an assist as the Thrashers snapped the Penguins' eight-game winning streak. Pittsburgh suffered its first loss since Dec. 21 against the New York Islanders.
Recchi was Atlanta's fourth shooter in the shootout. Slava Kozlov, Marian Hossa and Ilya Kovalchuk were stopped by Ty Conklin, who suffered his first loss in 10 decisions with Pittsburgh.
Conklin stopped 36 shots. He started each of the eight straight wins.
Kovalchuk scored his league-leading 37th goal in the first period for Atlanta. Kovalchuk has goals in four straight games.
The Thrashers outshot the Penguins 38-31, only the seventh time they have had more shots on goal than their opponent.
Crosby opened the scoring with a first-period goal, knocking in a rebound after Lehtonen stopped a shot by Ryan Whitney 5:23 into the game.
About 4 minutes later, Kovalchuk answered with a power-play goal on an assist from Recchi. Kovalchuk pumped his right fist after his shot from the left circle.
Crosby looked almost unstoppable as he gave the lead back to Pittsburgh early in the second period. Crosby skated around Eric Boulton in front of the right circle before skating behind the net, giving up the puck and then scoring on the pass from Kris Letang.
Crosby had his fifth two-goal game of the season and his first since Nov. 30 against Dallas.
Hossa earned an assist on a tying goal by Bobby Holik 1:40 into the third period. Hossa's shot was blocked by Conklin, but Holik followed by pushing the puck past the sprawling goalie.
Notes: The Thrashers played their second straight shootout, following a 3-2 home loss to Florida on Thursday.... Recchi has 16 points (seven goals, nine assists) in 17 games since joining the Thrashers.... Conklin had allowed no more than one goal in three straight wins and gave up two goals for only the second time in seven games.... Attendance was 18,545 for the Thrashers' fifth sellout.