"Last year we started out awfully, and we were out of it at Christmas time," said Hedberg, who made 40 saves and added an assist in his first start of the season to help send the Thrashers (4-1-0) to their best start in franchise history with a 4-2 win over the Buffalo Sabres on Saturday night.
"We learned from that, and we're trying to get as many points as we can early on here because we want to stay in this race."
That won't be hard to do if Atlanta continues getting production from star forward Ilya Kovalchuk, who scored twice to increase his total to seven, and stellar goaltending from both Hedberg and Ondrej Pavelec.
"I always expect to win," Thrashers coach John Anderson said. "I want to convey that to every guy on our team."
Hedberg continued his mastery of the Sabres by improving to 11-2-1 lifetime against Buffalo, and helped hand the Sabres (4-1-1) their first regulation loss of the season.
"We have a good team," said Afinogenov, who signed with Atlanta after nine seasons with the Sabres. "Our goalies are playing unbelievable for us and that helps make our leads safe."
The Thrashers got 12 of the game's first 13 shots in the opening 10 minutes, and jumped out to a quick 2-0 lead.
But after that sluggish start, Buffalo outshot the Thrashers 41-15 in the final 50 minutes -- including a 20-4 advantage in the third period -- but were thwarted continuously by the spectacular play of Hedberg.
"It was hard always coming back," said Buffalo forward Drew Stafford, who cut the Atlanta lead to 3-2 with 3:34 left in regulation only to watch Afinogenov clinch the game 17 seconds later with a splendid individual effort that was started by Hedberg. "We'd make a charge but then we'd let them get one right away."
Clarke MacArthur also scored for the Sabres. Buffalo entered the game as the lone team in the NHL yet to be defeated in regulation.
Patrick Lalime made his first start of the season, and finished with 23 saves in the loss.
"You can't start a game like that," Sabres coach Lindy Ruff said. "If you start a game like that you're asking for a loss. We didn't deserve to win."
Buffalo was again without high-scoring left wing Thomas Vanek, who missed his second straight game with an upper-body injury.
Kovalchuk opened the scoring on the power play nearly 7 minutes into the game with a wrister from the high slot that went into the top-right corner.
Kovalchuk tallied again for his second of the night 3 minutes later when he one-timed a shot from the slot after receiving a pass from Bryan Little.
"If you're going to hand their best player those types of opportunities, you're going to fail," Ruff said.
MacArthur cut the lead in half with his team-leading fourth goal of the season 6:56 into the second period, sending a slap shot from the outer edge of the left circle that handcuffed Hedberg.
Atlanta regained its two-goal edge 57 seconds later when White scored the Thrashers' second power-play goal of the game.
"We're happy to take this one," Hedberg said. "We have a lot of good pieces, now we have to keep working. It's the start we wanted."
Entering the game, the Thrashers had played the fewest games (four) in the league. ... Sabres C Adam Mair played in his first game of the season after having hip surgery. He replaced C Matt Ellis, who is out with a quad contusion. ... Three former Sabres -- Chris Thorburn, Eric Boulton and Afinogenov -- skated for the Thrashers. ... Atlanta has won the past five meetings with Buffalo.