Carolina's division lead is down to one point after the second-place New Jersey Devils won 2-1 against the New York Rangers on Thursday.
Frederik Andersen made 19 saves for the Hurricanes (47-18-9), who have lost three in a row (0-2-1).
"That's brutal, because we played well enough to win and we gave away the points at the end," Carolina coach Rod Brind'Amour said. "We just didn't get any breaks and then we took a breather at the end of the game, and it ended up in our net."
Walman one-timed Andrew Copp's pass from the point through traffic in front for the game-winner.
"That was just a great play by (Copp), really," Walman said. "We were going for broke, because there wasn't much time left. He made a really good pass and we had a screen in front."
David Perron had two assists for the Red Wings (33-32-9), two days after scoring a third-period hat trick in a 7-4 win against the Pittsburgh Penguins.
"He's a huge part of this team," Detroit coach Derek Lalonde said. "He only knows one way to play, and that's been important on a team where some guys have struggled for motivation since the trading deadline (on March 3)."