Oduya scored his first goal for Chicago with 5:56 left in the third period to snap a tie in the Blackhawks' 4-3 comeback victory over the Rangers on Friday night.
Chicago handed the Eastern Conference-leading Rangers their third straight loss and fourth in five games.
Oduya connected from the left point with a shot that sailed past Henrik Lundqvist on the glove side to give Chicago a 3-2 lead, its first of the game. Oduya was acquired from Winnipeg just before the trade deadline.
"Oduya had a great game," Kane said. "He scored the goal that should have been the winner. Forwards love to play with him. He's a guy who can get you the puck with speed."
Chicago's Patrick Sharp scored 1:02 before Oduya to cap a nifty passing play with Marian Hossa and Kane, and tie it at 2. Oduya also set up a goal by rookie Andrew Shaw in the second period to help Chicago win for the fourth time in five games.
"It was fun hockey at the end," Kane said. "These points are huge, especially against one of the best teams in the league."
Chicago's three-goal flurry in 6:05 span late in the third came after the Rangers limited the Blackhawks and controlled most of the game.
"We had the same kind of game as last time in here," Oduya said. "Struggling at the beginning, but a great turnaround and a great team victory."
The Rangers, who have given up 19 goals in their last five games, opened with a tightened defensive effort and seemed to be in command as the game wound down. Lundqvist, who wasn't heavily tested until late, made 18 saves.
"If you watch the third period, the game was going our way," New York coach John Tortorella said. "We were doing fine. We have a defensive mistake, someone falls down and they end up scoring, and then get another one after that. I thought we got back to the way we needed to play. I thought we had some sustained pressure. I thought we did some things along the walls. I thought we checked well.
"We did a lot of good things. We were finding ways to win earlier. We're finding ways to lose right now."
The game was the second this season between the Original Six teams. Chicago snapped a season-high, nine-game losing streak with a 4-2 victory in New York on Feb. 16.
The Rangers had several prime chances in the first period, but didn't connect until Anisimov opened the scoring with 47 seconds left following a botched Chicago clearing attempt.
When Kane couldn't handle the puck on the boards near the Chicago blue line, New York's John Mitchell slipped the puck to Anisimov alone in the slot. Anisimov took the pass with his back to Emery, then spun and tucked in a shot in the lower right corner.
The Rangers limited Chicago's offense for most of the second, but Shaw tied it at 1 with 5:32 left in the period on a tip of Oduya's shot from the left point.
Oduya fired into traffic, the puck struck the blade of Shaw's stick about 2 feet above the ice and flipped past Lundqvist.
A turnover at center ice led to Prust's goal at 7:11 of the third that gave the Rangers a 2-1 lead. Emery dropped to the ice to stop Ryan McDonagh's shot from the top of the slot. But Prust was wide open just to the left of the net and easily slipped in the rebound.
Then the Blackhawks rallied with three goals -- on three shots -- in a 6:05 span to take the 4-2 lead.
"Tonight, I thought we took a big step to playing closer to the way we've been playing in the past," McDonagh said. "But it just goes to show you, in the blink of an eye, it can get away from you. I don't really have an answer for why. It's a tough pill to swallow right now."
New York C Brandon Dubinsky sat out his second game after being injured in a fight with New Jersey's Ryan Carter early in a 4-1 loss Tuesday night at New Jersey. Dubinsky, who sustained a hand injury and a cut to the nose in the fight, is experiencing sinus pressure and is listed as day-to-day. ... Chicago C Jonathan Toews missed his ninth game because of an upper-body injury, believed to be a concussion. Toews skated for second straight day Friday morning. ... Blackhawks D Niklas Hjalmarsson returned after missing six straight games and 13 of 14 with a reported concussion.