Max Domi had two goals and an assist, and Seth Jones and Jake McCabe had two assists each for the Blackhawks (7-12-4), who were 0-7-1 in their previous eight.
Petr Mrazek allowed one goal on 22 shots before leaving following the second period with a groin injury. Arvid Soderblom replaced him and made five saves.
Richardson said they're hoping it will be a short-term injury for Mrazek, who missed eight games after sustaining a groin injury on Oct. 21.
"It's not the same one, so that's maybe a good thing," Richardson said. "I know a lot of times with injuries when you rehab one side the other side is not as strong. Hopefully after this he can be a little bit more balanced and make it through."
Mika Zibanejad had a goal and an assist, Artemi Panarin had two assists, and Jaroslav Halak made 16 saves for the Rangers (11-10-5), who have lost five of their past six games (1-4-1) and four in a row at home (0-3-1).
"It's a results league, you need to win hockey games," New York captain Jacob Trouba said. "It's an emotional game. You've got to play with some emotion, some energy. It's not just going to happen. You've got to go make it happen, and will it to happen. I think we could use a little more of that."
Reese Johnson gave Chicago a 1-0 lead on a deflection at 2:38 of the first period.
The Rangers felt Trouba tried to give them some emotion and energy with his physical play in the second period, when he had a big hit on Blackhawks forward Jason Dickinson at 2:58 and fought forward Jujhar Khaira 24 seconds later.
However, New York had a power-play opportunity wiped away after Zibanejad was called for slashing at 7:34, and less than one minute later, forward Ryan Carpenter was called for hooking at 8:24.
On the ensuing 5-on-3 power play, Kane scored on a rebound to make it 2-0 at 8:37. Domi then scored on the remaining power play with a wrist shot from the top of the left face-off circle to extend it to 3-0 at 9:37.
Chicago finished the game 3-for-4 with the man-advantage.