Ryan Callahan had a goal and three assists as the Rangers snapped a two-game losing streak, picking up two vital points in their fight to hold onto a playoff spot in the Eastern Conference. New York started the night clinging to eighth place.
Stepan broke a 2-2 deadlock in the third as he pounced on the rebound of Anton Stralman's shot from the left point and knocked the puck past Pavelec at 5:46.
Nash gave the Rangers a 4-2 lead at 13:07.
The Jets led 2-1 after dominating the opening period.
The Rangers struck first as Stepan slipped behind the Winnipeg defense to beat Pavelec 19 seconds in, New York's first goal in three games. The Rangers were blanked by identical 3-0 scores in their prior two games in Ottawa and Montreal.
The lead soon evaporated as Antropov, left all alone in the slot, swept Kyle Wellwood's centering pass between Lundqvist's pads at 1:15.
Winnipeg took the lead at 12:54 as Bogosian fired a point shot that appeared to deflect of someone before it flew past Lundqvist.
The Jets outshot the Rangers 11-7 in a period where they spent long stretches in the New York zone.
The Rangers were much better in the second period, outshooting the Jets 15-7 while pulling even on Callahan's brilliant short-handed tally at 3:11.
Callahan sped into the Winnipeg zone as Mats Zuccarello returned to the ice after New York killed off the first half a Jets five-on-three power play. Showing great patience, Callahan first deked a Winnipeg defender, and then Pavelec, to the ice before depositing a backhander.