Mario Ferraro had a goal and an assist, Michael Eyssimont had a goal and two assists, and James Reimer made 31 saves for the Sharks (14-25-11), who have lost the first four (0-2-2) of their season-high eight-game road trip that continues at the Pittsburgh Penguins on Saturday.
"We've had a season of incredibly disappointing losses," San Jose coach David Quinn said. "I just loved the way we played for really most of the game. Unfortunately, we've got a lot of practice in losing games in this fashion. I am very disappointed for our players, because I thought they did a really good job. [They] deserved a better fate."
Aho gave Carolina a 2-1 lead 17 seconds into the third period on a power play when he drove to the net and redirected a pass from Stefan Noesen with one hand on his stick.
Nick Bonino tied it 2-2 at 6:50 when he took a pass from Eyssimont while driving to the net and roofed a shot over Raanta.
"We process this type of game so much," Bonino said. "We're in every game we play. We're in every game and we find ways to lose them. It's not good enough. I don't know if [we were] overwhelmed, [but] tons of guys in this room, we've played in some pretty big situations before."
Eyssimont, who was claimed off waivers from the Winnipeg Jets on Jan. 6, scored his first goal with San Jose at 11:15 to make it 3-2 before Ferraro extended it to 4-2 at 18:08 with an empty-net goal.
Aho then scored 15 seconds later to cut it to 4-3 at 18:23 when he got behind the defense after receiving a pass from Teuvo Teravainen.
"We believe in each other, and there's no quit in this team either," Aho said. "We work hard until the game is over and obviously, that was the case tonight."