Toronto (8-8-3) has scored first in its past five home games, and this was the first time it lost when scoring first at home (6-1-0).
On a Hurricanes power play, Derek Ryan chipped a puck over top of Andersen and it went off Skinner's skate to tie it 1-1 at 17:21.
"They scored on their power play, we didn't," Maple Leafs coach Mike Babcock said. "We gave up a shorthanded goal, so there's the game right in itself. In saying all that, I thought it was a contested game, there was no room, there was lots of battles. I think these are games we have to get better in and find ways to win."