The Thrashers, three points out of the final playoff spot in the Eastern Conference, squandered a pair of two-goal leads for the second game in a row but still managed another vital win.
Antropov scored off a pair of deflections in front of the net, including a tiebreaking power-play goal with 16:04 remaining in the third period.
Armstrong added two goals less than 5 minutes apart to put it away for the Thrashers, who had lost six in a row before beating a pair of teams that appear headed for the playoffs, Buffalo and Ottawa.
The Senators are struggling, though. They have lost seven of eight games since the Olympic break, including the last four.
Atlanta reclaimed the lead after Andy Sutton, who had a rough night, delivered a cheap shot to Eric Boulton near center ice and was sent off for elbowing. With a man advantage, Tobias Enstrom fired a slap shot that Antropov deflected past Brian Elliott for his 21st goal of the season.
Armstrong clinched it for the Thrashers. First, he stole an attempted clearing pass by Chris Phillips and ripped a shot over Elliott's left shoulder for an unassisted goal with 14:26 left. Then, after Armstrong had a shot blocked in front, he scrambled in front of the net, took a return pass from Jim Slater and flipped it past Elliott with 9:40 left.
Atlanta scored on its first three shots on goal in the third period.
The Thrashers had leads of 2-0 and 3-1 before the Senators tied it with two goals just 43 seconds apart late in the second period.
Atlanta goalie Johan Hedberg was livid about the first one, believing he was interfered with by Jarkko Ruutu after stopping the initial shot by Chris Campoli. The puck slid wide of the post, and Ruutu got a piece of Hedberg at the top of the crease going after the loose puck.
Hedberg fell over and couldn't get back in time as Ruutu scooped up the puck from behind the goal line, then tucked it just inside the post for his 11th goal. The goalie complained bitterly and had to restrained by a linesman as he attempted to get at referee Stephane Auger.
Still seething about that call, Hedberg got even angrier when Phillips picked off an errant clearing pass and fired a screened shot past the goalie for the tying goal less than a minute later. Not long after, Hedberg made a save and shoved as a Senators player just for getting near the net.
But Hedberg came up big most of the night. Among the 36 shots he stopped was a brilliant pad save on Jason Spezza, who cut in alone on the net midway through the third.
Just 2½ minutes into the game, Sutton let a long clearing pass slip between his legs as he backed up near the Ottawa blue line. Evgeny Artyukhin scooped it up, sped in all alone on Elliott and slid in a backhander.
Jim Slater scored for the second game in a row to make it 2-0 early in the second. After Chris Kelly's goal for the Senators halved the lead, the Thrashers stretched it back out to a two-goal advantage on Antropov's first of the night.
Elliott made a difficult stop on Maxim Afinogenov at the side of the net, but the Thrashers winger grabbed the rebound and passed off quickly to Pavel Kubina at the top of the circle. He blasted a shot that was deflected in by Antropov before the scrambling goalie could get back in position.