Kovalchuk staked the Thrashers to an early 2-0 lead with his first goal, restored the two-goal lead with 13:40 remaining and turned the game into a rout with a final goal 3 1/2 minutes later that gave him his second hat trick and 11th goal of the season.
His first two goals were from just inside the blue-line. Kovalchuk cocked his stick, took passes from his teammates and fired shots with such force that he went down to his right knee for extra leverage.
Kovalchuk's third goal was from a little closer in, but he again took a pass and fired a blistering shot before Bruins goalie Tim Thomas had time to react.
Slava Kozlov and Marian Hossa also scored for the Thrashers, who have bounced back from losing two straight in regulation with a three-game winning streak.
Hedberg has been in the net for all three wins, taking over after No. 1 goalie Kari Lehtonen had a poor outing against Carolina last week. The backup played so well in road wins over Washington and the New York Islanders that he got another start against the Bruins, leaving Lehtonen on the bench.
Patrice Bergeron scored twice and Brad Boyes added a short-handed goal for Boston.
Struggling to keep up with the home team, Boston picked up five penalties in the first period. The Thrashers wasted no time capitalizing on their first two power-play chances, both of them with Paul Mara in the penalty box for hooking.
Just 11 seconds after Mara's first penalty, Kozlov worked the give-and-go to perfection with Hossa, who was parked behind the net. When Mara was sent off again, the Thrashers needed all of 20 seconds to find the net. From just inside the blue line, Steve McCarthy sent a cross-ice pass to Kovalchuk, his stick was already swinging back before his teammate let go of the puck.
The Thrashers finished the first period with a commanding 21-8 lead in shots on goal. Kovalchuk had six of them himself.
The Bruins pulled to 2-1 early in the second period, taking advantage of an interference penalty on Jon Sim. Like the Thrashers, they scored early in the power play, with Bergeron deflecting Mara's slap shot over a sprawled Hedberg 20 seconds into the man advantage.
But Kovalchuk's two goals - sandwiched around Hossa scoring on a breakaway after he flipped a bouncing puck around defenceman Andrew Alberts - gave the Thrashers a commanding 5-1 lead.
Notes: Atlanta appeared to score in the second period on yet another power play. But it was waved off when the replay showed Hossa punching the puck in with his left glove. ... Boyes scored a short-handed goal.