Trailing 1-0 after the first period, the Hurricanes tied it 1:21 into the second. After Skinner beat out an icing call, Dwyer fed Jordan Staal, who was alone in front, for his first goal with the Hurricanes since being acquired from Pittsburgh in June. Staal also assisted on Dwyer's third-period goal.
Eric Staal then hit the post with a drive a few minutes later. The Hurricanes rebounded from a sluggish opening period to grab momentum with the first nine shots of the second.
The Hurricanes captain had better luck with his next chance, giving Carolina (4-4) the lead with his seventh goal of the season at 10:21 on the power play.
"I felt really comfortable at the start of the game," Ward said. "I expected they were going to throw a lot of shots at the net, and I had to be ready. It took a little bit to get our legs but to walk into that first intermission down one we really took over the second.
"We were able to get our feet moving and capitalize on some opportunities."
With Toronto's Jay McClement serving a penalty for unsportsmanlike conduct after giving Ward a snow shower, Eric Staal skated out from the corner and sent a cross-crease pass that deflected in off defenseman Mike Kostka.
"The first couple shifts of the second period, we turned the puck over at the offensive blue line and it started to deteriorate then and we started to play a lot more in the defensive zone," Maple Leafs coach Randy Carlyle said. "On faceoffs we didn't do a very good job of blocking out to retrieve pucks, and we let them jump through a few times.
"The momentum went in their favor and then we got ourselves behind the eight-ball with maybe focusing on some of the things that were going on in the game other than how we were playing and how we needed to play to be effective."
The Maple Leafs (4-5) thought they had tied it with 1:16 left in the second when Kostka's shot from the point deflected in off Tyler Bozak. But after a video review, officials ruled the Toronto center kicked the puck in past Ward.
"I don't think I kicked it," Bozak said. "Tough call and there's nothing we can do now. We have to fight through adversity and things like that. Unfortunately it didn't go our way."
The home crowd was further incensed when the Maple Leafs were assessed back-to-back penalties to close out the period.
With Carolina on a 5-on-3 man advantage to start the third, Faulk finished off a pretty tic-tac-toe passing play 43 seconds in with a goal that also went to a video review.
The Maple Leafs fell to 1-4 at home.
"We can play for stretches in this building but it seems that when it starts to go the other way on us we don't seem to be able to pick ourselves back up and say, 'Hey stop it.' This is what we've got to do to correct it," Carlyle said. "The turnovers are the most disturbing thing for me.
"As a coach you want to limit those turnovers and those are the most disturbing things."
Toronto's Phil Kessel, who has no goals through the first nine games of the season, had a great chance to net his first during a power play but he was denied by Ward with just over 13 minutes remaining.
The Maple Leafs continued to press, but Ward stopped Nazem Kadri and Bozak to maintain the Hurricanes' two-goal edge. Carolina put the game out of reach when Dwyer beat Reimer with a quick shot at 9:58.
Frattin opened the scoring 5:44 into the game. Kadri carried the puck over the blue line on a 2-on-1. After fanning on his first attempt, he fired a weak shot that Ward kicked into the slot.
Frattin pounced on the rebound and scored his fifth goal in six games since being recalled from Toronto of the AHL.
Frattin has made the most of his opportunity on a line with Kadri and Leo Komarov.
Reimer couldn't explain why the Maple Leafs have struggled at home. The troubling trend dates to last season.
"You come home and this is the place you want to win," he said. "I'm not quite sure what the reason is and I don't know if anybody does have the reason.
"It's the million-dollar question and we don't like it. We don't like it one bit."
Kadri was hurt after blocking a shot in front of Reimer in the first period but didn't miss a shift. ... Referee Marc Joannette was hit by a clearing shot from Maple Leafs D Dion Phaneuf in the second period. He received attention from the Maple Leafs training staff and returned later in the period. ... The Maple Leafs open a three-game road trip on Tuesday in Washington. ... The Hurricanes visit Ottawa on Thursday.
Copyright by STATS LLC and The Associated Press
Arena: Air Canada Centre Location: Toronto, Ontario
Referees: Marc Joannette, Graham Skilliter Linesmen: Derek Amell, Scott Cherrey
Attendance: 19,072 (101.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Matt Frattin (5)
Assists: Nazem Kadri, Leo Komarov
Jordan Staal (1)
Assists: Patrick Dwyer, Jeff Skinner
Eric Staal (7)
(Power Play) Assists: Jiri Tlusty, Tim Brent
Justin Faulk (2)
(Power Play) Assists: Jeff Skinner, Alexander Semin
Patrick Dwyer (3)
Assists: Jordan Staal, Jeff Skinner