Alex DeBrincat had a goal and an assist, and Dylan Larkin had two assists for the Red Wings (35-33-7), who have earned a point in three straight games (2-0-1).
Detroit is four points behind the Montreal Canadiens for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
“We’ll enjoy this win tonight, but if you look at our schedule, it doesn’t get any easier," Kane said. "Tomorrow, we’ll start getting ready for Florida on Sunday.”
Cam Talbot made 30 saves for Detroit, which blocked 25 shots.
“I don’t think a goaltender can beat that team alone, it has to be a team game,” Red Wings coach Todd McLellan said. “We made some mistakes and they made us pay, but we sold out, blocked shots, got some really good penalty killing and made some big saves.”
Jackson Blake, Eric Robinson and Brent Burns scored for Carolina (46-25-4), which had won three straight. Pyotr Kochetkov made 16 saves.
“We got behind early, but then we dug in and played a great game,” Hurricanes coach Rod Brind’Amour said. “We just had a couple bad turnovers in the second period.”
The Red Wings scored twice in 26 seconds in the first period, then got two goals in 21 seconds in the second period.