It was a much-needed win for Chicago as the team snapped a nine-game losing streak, its longest in five years, and also stopped an 11-game road skid.
The last road win for Chicago came on December 14 at Minnesota and the team had gone 0-6-1 on its nine-game road trek coming into the game.
Nick Leddy and Patrick Sharp also scored while Corey Crawford stopped 22 shots for the Blackhawks, who won for the first time in New York since December 11, 2002 to snap a three-game skid as the guests.
"We have to keep going here because we put ourselves in a tough situation," said Towes. "We need to keep digging our way out of this hole and play hard."
Chicago blitzed New York for four goals over the first 9:38 of the game and the first came on a penalty shot when Dan Girardi closed his hand on the puck in his own crease.
Toews skated in on the free chance and buried it through the five-hole for a 1-0 lead just 65 seconds in.
Just 62 seconds later, it was 2-0 as a one-timer from Leddy in the high slot made its way through a screen.
At exactly four minutes, the Blackhawks scored again when Sharp was sprung on a short break down the left wing and his wrist shot trickled behind Biron for his 23rd of the year.
Hossa capped the burst when he took a lead pass near the blueline and buried a wrister for his 22nd of the season.
"Just a bunch of miscues we had early on and they were able to bury all of their chances," said Staal.
New York got one back 3:04 into the second when Staal blasted a shot from the left point to make it a 4-1 game.
It was a two-goal game with 4:45 to play when Ryan McDonagh skated the puck down from the left point and passed it to Hagelin for the redirect past Crawford.
However, the Rangers were unable to get any closer despite pulling Biron for the extra attacker with over two minutes to play.
Chicago plays the final game of its nine-game trek in Columbus on Saturday...New York plays in Columbus on Sunday...Neither team scored on the power play as New York failed on seven chances and Chicago came up empty on its three opportunities.