The Rangers shook off an empty two-game trip to Florida that broke their 13-game point streak (10-0-3).
New York also slowed down the Sidney Crosby-less Penguins, who had won three in a row and racked up 14 goals in their previous two victories without the injured captain.
Crosby, the reigning NHL MVP and scoring champion, missed his third straight and 24th of 27 because of a high ankle sprain, and is expected to sit out at least one more. He watched the game from a suite along with his father and several fathers of his teammates, who made the trip with the Penguins.
The Rangers kept Evgeni Malkin, the league's second-leading scorer, without a point and recorded 30 shots on Ty Conklin.
Fredrik Sjostrom snapped a 2-2 tie in the second period for New York, which moved two points ahead of Boston for sixth place in the Eastern Conference. The Rangers are third in the Atlantic Division, four points behind Pittsburgh and five in back of New Jersey, their road opponent on Wednesday night.
Sjostrom stole the puck in the Penguins' zone, just 44 seconds after Pittsburgh tied it, and scored off a mini breakaway at 3:55.
Avery and Ryan Callahan scored 40 seconds apart in the opening period to stake the Rangers to a 2-0 lead, but that evaporated early in the second when Jarkko Ruutu and Jordan Staal answered 1:33 apart.
Martin Straka made it 5-2 with 8½ minutes remaining.
