After netting just four goals in his first 130 NHL games, Harrison has scored 10 in his last 76 contests, including three game-winners. Against Buffalo, he fired a slap shot from the right point after Eric Staal won a faceoff, and the puck beat the Sabres' Ryan Miller on the short side.
"I just put a puck to an area," Harrison said. "Maybe get an opportunity to score, but also to generate a rebound and generate some traffic. You shoot enough of them, and eventually they go in."
Harrison, who turned 30 in November, believes his offensive game has perked up because he has gotten older.
"I haven't changed my game," he said. "I've developed a little more confidence and been able to generate better opportunities to get into position to get the puck and shoot the puck."
Miller was frustrated at his play on Harrison's goal.
"I've got to find (it) through the traffic," Miller said. "I didn't pick up on the release, saw it kind of halfway through. I was just a little too far to the side."
Alexander Semin tied it for the Hurricanes early in the third period, and Jeff Skinner scored an empty-net goal for Carolina (2-2-0), which has won two straight games. Dan Ellis made 40 saves in his first start for the Hurricanes.
Semin's goal was his first goal as a Hurricane, connecting on a wrist shot during a power play 3:31 into the third period.
Thomas Vanek scored for Buffalo (2-1-0), losers of two in a row. Miller stopped 39 shots in his first loss of the season.
Vanek continued his torrid start to the season, breaking a scoreless deadlock with a power-play goal 1:56 into the third. He snapped a shot from the left circle after picking up the puck near the corner. Vanek has been on the ice for all 11 goals scored by Buffalo this season, and his nine points (three goals, six assists) in the first four games tied a team record.
Buffalo's chances to tie the game late were hindered when Vanek was assessed a cross-checking penalty with 2:09 remaining. Despite getting two shots while down a man, they eventually allowed Skinner's empty-net goal.
"I thought at the start of the second period, we had five or six good opportunities," Buffalo coach Lindy Ruff said. "We missed on a few, but we gave up some beauties tonight again. Some plays by our defense hurt us in a couple situations."
Before the third period, the teams battled evenly, with Carolina getting the best chance to take a lead about 6 minutes into the second period. Staal rang a wrist shot off the goalpost and Miller followed with a sharp save on Joni Pitkanen, who one-timed the rebound.
Ellis was superb in his first NHL start since Dec. 21, 2011. The 40 saves were his most since recording 41 with Anaheim at San Jose on Oct. 17, 2011.
"It was wonderful," Ellis said. "You're thankful to be back and be able to make some saves and help your team get a win and create some momentum."
NOTES: Carolina went 2 for 5 on the power play, and Buffalo was 1 for 4 with the man advantage. ... Ellis made his second career appearance against Buffalo. The veteran of 167 NHL contests had faced the Sabres for just 25 minutes in a relief performance with Nashville on Feb. 27, 2008. ... Buffalo is the only NHL team with which the Hurricanes have never made a trade. The last transaction between the clubs occurred in October 1989, when the franchise was based in Hartford and Bo Mikael Andersson went to the Whalers in a waiver draft deal.