The Thrashers were 0 for 13 over a three-game stretch with a man advantage, including their first power play against Anaheim. But Afinogenov scored from the right circle 4:03 into the third period, rewarding the Thrashers for their recent emphasis in practice on the power play.
"The nice thing was that it was a power-play goal that won it for us," Anderson said. "We talked about the importance of getting one goal a game on the power play. It really makes a difference."
Anaheim had killed 21 of its last 23 penalties before Afinogenov's go-ahead shot through Jonas Hiller's legs.
"Before the game we spoke about we wanted the power play to get going and how it's going to win the game," Afinogenov said. "We just tried to shoot more and I think it's working. We got a couple of shots.
"The puck was bouncing there for me. I just tried to put it into the net and it worked."
The Thrashers began the night ranked 18th in the league with their 17.7 percent success with a man advantage.
"We've been working on that lately," Hedberg said. "When you try to do too much, sometimes you overdo something."
The Ducks were stopped on their four power plays.
"Our first power play we had seven or eight shots," said Bobby Ryan, who had an assist on Eminger's goal. "We lost momentum. Everybody was trying to do too much."
Hedberg allowed one goal in his third straight game, but the Thrashers' poor production on their power play helped lead to losses in the first two game.
"It's a big win for us tonight," Hedberg said. "We've been deserving to win the last few weeks, and tonight we managed to get the extra goal. Hopefully that's what we need to put us on a roll here."
The Thrashers are 5-4-1 since ending a nine-game winless streak. The Ducks lost for the third time in 11 games.
Anderson said the Thrashers "thought we've played very well" even while losing three of their last four before facing the Ducks.
"The last three or four games, we certainly didn't reap the reward," Anderson said. "Tonight was a breath of fresh air. We played a tight, low-scoring game and we won."
The Thrashers won for only the third time in regulation when scoring no more than two goals.
The Thrashers were stopped on their final two opportunities with a man advantage, leaving them 1 for 4 in the game.
Hiller had 32 stops.
"He played well enough to keep us in the game," Anaheim's Ryan Getzlaf said. "It's frustrating. Maybe we over-handled the puck a little bit."
Atlanta's Chris Thorburn left after he was hit in his face by the puck 5:37 into the third period. Thornburn fell to the ice before heading to the locker room. He returned later in the period.
The Thrashers improved to 2-4 in Atlanta against the Ducks with their first home win in the series since Dec. 5, 2003. Anaheim leads the overall series 7-5. ... Ducks C Saku Koivu of Finland, one of the team's eight Olympians, returned after missing four games with a sprained right knee. ... Thrashers F Slava Kozlov was a healthy scratch for the second straight game. He had a franchise-record 251 consecutive games played before he was held out of Saturday's 2-1 loss at Tampa Bay.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Gord Dwyer, Kelly Sutherland Linesmen: Derek Amell, Brian Murphy
Attendance: 12,984 (70.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Colby Armstrong (9)
Assists: Evander Kane, Ron Hainsey
Steve Eminger (2)
Assists: Corey Perry, Bobby Ryan