New York, which began the day eighth in the Eastern Conference, moved within four points of fourth-place Philadelphia. The teams have two meetings remaining.
Fredrik Sjostrom scored a wraparound goal at even strength to make it 4-1, giving the Rangers their fifth win in nine games (5-3-1) since John Tortorella replaced fired coach Tom Renney.
Henrik Lundqvist made 24 saves for his 31st win, allowing only Simon Gagne's power play goal in the second. Earlier this week, Lundqvist became the first goalie to post 30 victories in each of his first four NHL seasons.
Avery staked the Rangers to a 1-0 lead in the first period, stretching his goal streak to three games, and added his second in the third period while New York enjoyed a 5-minute power play.
Flyers defenseman Braydon Coburn was ejected in the closing seconds of the middle period after high-sticking Antropov near center ice, drawing a major penalty. New York scored only once on the advantage, but coupled with Andrew Alberts' charging infraction on Avery, Philadelphia was short-handed for the first 7 minutes of the third as it tried to rally.
Avery has four goals in seven games since rejoining New York, topping the three he had in 27 games earlier this season with Dallas.
One day after Martin Biron made 39 saves in beating the Rangers 4-2 in Philadelphia, he gave way to backup Antero Niittymaki, who stopped 35 shots.
Antropov gave New York its second one-goal lead 8:27 into the middle period when he snapped a shot in off the post from the right circle.
New York grabbed a 1-0 edge in the first period for the second straight game against the Flyers. Avery got his stick blade on Derek Morris' shot in front and tipped the puck under the crossbar, popping up the water bottle that sat on top of the net with 2 minutes left. He went into his trademark arm-pumping glide in celebration.
The Rangers had 14 straight failed power-play chances before Avery broke the drought. Antropov's goal gave them two man-advantage goals for the second time in six games after they had gone 16 straight without doing it.
Gagne tied it for the Flyers 4:32 into the second period. With his back to the net in between the circles, Gagne deflected Mike Richards' shot from the right point past Lundqvist.
Avery got to a loose puck in front to make it 3-1 at 2:45 of the third, and Sjostrom closed the scoring with 9:49 left.
Notes: It was the Rangers' 150th consecutive home sellout. ... Antropov has three goals in six games since being acquired from Toronto at the trade deadline. ... Philadelphia is 7-4-3 in the second half of back-to-back games. New York had dropped five straight back ends and improved to 7-5-1. ... The Flyers' have the NHL's seventh-best penalty-killing unit.
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