Jimmy Howard made 34 saves for Detroit (7-16-3), which was also playing the second game of a back-to-back (lost 5-1 to the New Jersey Devils on Saturday) and is 0-4-2 in its past six games.
"We couldn't get out of our own end," Red Wings coach Jeff Blashill said. "When you have to defend that much on the second half of a back-to-back, it is really tough. Defense is harder to play than offense."
Aho gave the Hurricanes a 1-0 lead at 10:37 of the second period. Aho skated to the top of the left circle and shot wide off the end boards before getting his rebound in the crease when Howard couldn't cover the loose puck. Andrei Svechnikov had the secondary assist on the play to extend his point streak to eight games (five goals, seven assists).
"I was trying to bank the puck off the boards to [Teravainen], but I guess he can't skate as fast on the second night of a back-to-back," Aho joked. "That meant I had to go get it myself."
Nino Niederreiter took Carolina's only penalty at 17:33 of the third period, but Teravainen scored shorthanded into an empty net to make it 2-0 at 18:47.
The Red Wings didn't get a shot on goal during the 6-on-4 advantage.
"We were really good in the neutral zone all night and then we took a penalty right at the end," Brind'Amour said. "This was a game where everyone stepped up and made plays when we needed them."
Carolina outshot the Red Wings 24-8 over the final two periods, including 13-3 in the third.
"We didn't make it hard enough on their defensemen and their goalie," Red Wings forward Dylan Larkin said. "They've got big defensemen who make it tough to get set up in their zone, but we've got to be able to get five guys attacking and create chances."
Said Aho, "We were trying to get the puck deep and grind away at them in their end so they couldn't play offense. They were pretty gassed when they finished their shifts. That's how we try to play every night."
Detroit played without forward Anthony Mantha, its leading scorer, because of a lower-body injury he sustained in the loss to the Devils.
"We didn't have an offensive spark and Anthony's been our best offensive player this year," Larkin said. "We missed him for sure, but we don't know how long he's going to be out so we can't start thinking about that."