The Hurricanes went ahead 1-0 on the power play after a deflection caught Markstrom moving and left Niederreiter with an open net at 1:54.
Leivo tied it 1-1 with a redirection at 2:57, and Baertschi finished off a three-way passing play with Brock Boeser and Elias Pettersson at 5:14 to put Vancouver ahead 2-1.
"We gave ourselves a chance there in the second period, and right after that, we just kind of took our foot off the gas and just gave up way too many Grade A opportunities in our slot," Horvat said. "[Markstrom] didn't have a chance."
McKegg tied it 2-2 at 6:53, one-timing a pass from Saku Maenalanen from below the goal line, and Niederreiter scored his second goal on a pass from Aho from below the goal line to make it 3-2 at 13:17.
Niederreiter has four goals in four games with Carolina since being acquired from the Minnesota Wild in a trade for Victor Rask on Jan. 17.
"It's definitely a lot to take in but, at the same time, I know how good Aho is and [Justin] Williams is," Niederreiter said of his new linemates. "They are great playmakers, and for me, it's just trying to find the open ice and like tonight a terrific pass by Aho and I had a chance to do the rest."