The Southeast Division leaders ended their two-game losing streak, but not before trailing 2-0 as the second period neared the midway mark. The Thrashers then scored three goals in less than 3 1/2 minutes, helped by some odd bounces off Capitals, to take the lead.
Hedberg was making only his second start and third appearance of the season, replacing Kari Lehtonen, who was pulled from Atlanta's previous game after giving up four goals on 13 shots.
Dainius Zubrus scored twice for last-place Washington, which has lost all three games against Atlanta this season by the same score, although one ended in a shootout and another in overtime.
Zubrus' second goal of the game and ninth of the season was scored with 5.3 seconds remaining in the second period. It came after a goalmouth scramble and was initially waved off because officials thought a hand pass was made, then awarded after a video review.
So it was 3-3 heading into the final period - and Rucchin changed that right away.
Jon Sim, who scored Atlanta's first goal, brought the puck to the blue-line, where he passed it to Rucchin. No one from the Capitals really challenged the centre, and Rucchin lifted a shot between goalie Olaf Kolzig and the near post for his second of the season.
From there, Hedberg was steady enough, finishing with 27 saves, seven in the third period. He avoided having to face a late power play, when Sim was sent to the penalty box for tripping Calder Trophy winner Alex Ovechkin with less than five minutes left. The Capitals were whistled at the same time for having too many men on the ice.
Hedberg was shaky early. Washington went ahead thanks to Zubrus' power-play goal 12:10 in, and Chris Clark's short-handed breakaway score 1:36 into the second period. Clark's goal came eight seconds after teammate Richard Zednik was whistled for hooking.
Sim's seventh goal opened Atlanta's three-goal spurt, when he one-timed a shot off a nice pass from Ilya Kovalchuk 11:35 into the second period. Greg De Vries was credited with the goal that made it 2-2; he began the play with a pass that went through defenceman Jamie Heward's legs to Rucchin, whose shot bounced around off a couple of players, including De Vries, before getting past Kolzig.
Only 35 seconds later, Atlanta scored again. Vyacheslav Kozlov was credited with that one after another mess in front.
Notes: It was the first time Washington lost in regulation after scoring first. The Capitals had been 3-0-2 when taking a 1-0 lead. ... Toronto's Barenaked Ladies sang the national anthem. ... Atlanta is in the midst of playing seven of eight on the road. ... Last season, when Zubrus scored a career-high 23 goals, he didn't get No. 9 until Jan. 8, in Washington's 40th game. ... Washington completed its first winning October (4-3-4) since 1997-98, when the Capitals reached the Stanley Cup finals.