The Jets earned their 10th road victory of the season and increased their division lead to six points over Carolina.
"We're trying to forget about that Washington miniseries as much as possible," Kane said of the 4-0 and 6-1 defeats on consecutive nights.
"I think we've responded here in these last two games real well. We knew we couldn't dwell on what happened with Washington and we needed to move on and move forward."
The win over the Hurricanes, which came on the heels of a 3-2 home victory over Tampa Bay on Sunday, is the first of a stretch in which the Jets play five of six on the road.
"We knew the implications going in," Kane said. "It was a big game for both teams, but it's not going to be the last one, that's for sure."
Kane assisted Olli Jokinen's goal in the first period and goals by Tobias Enstrom and Alexander Burmistrov in the second. Kane was credited with a third-period goal when Carolina defenseman Jamie McBain swatted at the puck and knocked it into the net past Justin Peters.
Ondrej Pavelec had 38 saves for Winnipeg.
"They had some chances," Pavelec said. "I think they played really well. They did a great job getting traffic in front of me. Sometimes it goes this way."
Jiri Tlusty scored his 14th of the season for Carolina, which is on an 0-5-1 slide that includes three consecutive 4-1 losses at home.
With the Jets ahead 2-1 and 3:21 left in the second period, Burmistrov was credited with a goal after shooting once, having the deflection bounce to him chest-high and then into the net. After a lengthy review, the goal stood to make it 3-1.
Enstrom blasted a shot over Peters' left shoulder at 11:31 of the second, eight seconds after Jordan Staal was called for high sticking.
Tlusty opened the scoring at 6:06 of the first. Riley Nash passed from behind the net to Tlusty, who one-timed it past Pavelec.
Winnipeg tied it at 13:44 of the first. Kane poked the puck free near the Winnipeg blue line and raced in on a 2-on-1 break. He slid the puck to Jokinen, who beat Peters for his sixth goal of the season.
"When the puck drops, that's when you've got to perform," Carolina coach Kirk Muller said. "Not at the morning skate, not yesterday. It's all about playing, and we didn't have it tonight. There's no excuse for that."
The Hurricanes placed forwards Jussi Jokinen and Tim Wallace on waivers earlier Tuesday. Jokinen has five goals and five assists in 30 games, and Wallace has one goal in 21 games. Both are minus-7 for the season. Jokinen is in the second of a three-year contract that pays $3 million a season. ... Carolina's Alexander Semin played his 500th NHL game. ... The teams played the second of four meetings in the lockout-shortened season. The remaining two games are in Winnipeg. ... The Jets improved to 10-6-2 on the road, and the Hurricanes fell to 7-9-0 at home. .. Carolina fell to 8-2-2 when scoring first.