Semin tied it at 2 on a power play with 8:12 left, and Tlusty scored with 6:17 to go.
Jeff Skinner had a first-period goal — his 26th — to help Carolina win its second in a row after losing seven of eight. Nathan Gerbe had an empty-net goal with a second left.
Cam Ward made 21 saves, making his second consecutive start after backstopping the Hurricanes to a 3-1 victory over the New York Rangers on Tuesday night.
Tyler Ennis scored on a penalty shot and Drew Stafford added a goal for Buffalo. Michal Neuvirth made a season-high 51 saves in his second start for the Sabres since being acquired in a trade with Washington on March 5.
When things aren't going well for us in this city [Toronto], I think there is a lot of overanalyzing going on. You've got the most passionate fans in the world here and a lot of (media) coverage, so you know there's going to be a lot of people giving their two cents worth on us.
— Toronto Maple Leafs forward James van Riemsdyk after a win against the Tampa Bay Lightning on Thursday