Eric Belanger had a goal and an assist and Scott Mellanby also scored for the Thrashers, who set a franchise record with their 18th road victory. Shean Donovan and Brad Boyes each scored for Boston, which lost its second straight following a four-game winning streak.
Hossa snapped a 2-2 tie 7:28 into the third period when he took a drop pass from Belanger and fired a quick slap shot through a crowd and past Boston goalie Tim Thomas.
Zhitnik and forward Keith Tkachuk made their Atlanta debuts after being acquired in separate trades this weekend.
With the win, the Thrashers improved to 3-7-2 in February and pulled to a point behind Southeast Division leader Tampa Bay. Atlanta had lost six of seven entering the game to tumble from first place in its division to sixth in the tightly bunched Eastern Conference, with four teams battling for the final three playoff spots.
One of two franchises in the NHL (along with Columbus) never to make the post-season, the Thrashers acquired Zhitnik and Tkachuk for a late playoff push. The bold moves - Atlanta gave up right winger Glen Metropolit, top prospect Braydon Coburn and three draft picks - paid early dividends.
After Donovan's 100th career goal gave the Bruins a quick 1-0 advantage, Zhitnik assisted on Mellanby's goal to tie it at 1 with 5:25 left in the first period.
The teams then traded goals before Hossa's game-winner.
Kari Lehtonen recovered from a shaky first period to save 22 shots, including six in the third period. He held the Bruins scoreless after the first period.
Thomas stopped 17 shots for the Bruins, who squandered leads of 1-0 and 2-0 to remain tied for 11th in the Eastern Conference.
Notes: Atlanta committed just one penalty through two periods, taking advantage of four Boston penalties with a pair of power-play goals in those periods. ... Atlanta plays 11 of its last 17 games at home. ... Boyes extended his point streak to five games. He has four goals and three assists during that span. ... Boston outshot Atlanta 24-20.