"Finally luck shifted a bit," Boyes said with a grin.
Boyes also scored in regulation, while Tim Thomas made 23 saves and was perfect in the shootout for Florida, which won on the road for the first time since Dec. 19.
The winner meant extra for Boyes against his former teammate Enroth.
"Being here and going against him in practice a lot, he was showing me glove," Boyes said. "He was kinda waving it to me like he was onto me and he knows where I go. I have trouble with guys that I played with so it was nice to get it on him. I like that one."
The Panthers carried much of the play, outshooting Buffalo 35-24, but the sound of puck on metal was on a loop. Tomas Fleischmann hit the goal post twice in the third period, and Drew Shore also put one off the pipe in the frame.
"It would've been nice if a few posts counted as a goal," said defenseman Brian Campbell. "If you hit eight posts, maybe you get a goal or something."
Jamie McBain scored for Buffalo, whose new general manager Tim Murray got a closeup view of the tough rebuilding job ahead of him and special adviser Craig Patrick, introduced earlier Thursday by team President Pat LaFontaine.
The Sabres squandered a 1-0 lead and wasted a strong performance from Enroth, who was named to the Swedish Olympic team on Tuesday.
"I wanted to go out there and show everybody that I earned it," Enroth said.
Enroth is 1-9-3 this season, but the Sabres have scored just 17 goals in his starts and been shut out thrice. He couldn't explain the lack of goal support.
"I'm running out of answers on those questions," Enroth said.
The loss ended a five-game home win streak for Buffalo, who is still 6-0-2 in its last eight at First Niagara Center.
Florida started the game well, with eight shots on Enroth in the first 4:35 of play. Thomas then stopped a one-timer from Brayden McNabb about five minutes into the game.
Buffalo had the game's first power play after an interference call against Ed Jovanovski, and Thomas made a sprawling save on Jamie McBain to keep the game scoreless.
"They got some great chances, some great looks," said Florida head coach Peter Horachek. "Timmy was rock solid, he kept us in the game."
After play was whistled dead because of a scrum in Florida's crease, John Scott tossed the puck in the net and received a penalty for unsportsmanlike conduct.
Enroth saved a shot by Alexander Barkov on the ensuing power play and made 13 saves in the period as Buffalo was outshot by five.
Buffalo broke through in the second period when McBain streaked into the slot to collect Steve Ott's pass and fired low past Thomas' right pad at the 5:13 mark.
Brian Flynn had a breakaway moments later but Thomas smothered the shot to keep the deficit 1-0. Buffalo had trouble finding momentum despite the lead and killing off an abbreviated 5-on-3 penalty.
"Usually when you kill a big penalty kill, you get some momentum, but I don' t know," Enroth said. "It's tough to win with this team."
Florida nearly equalized at the start of the third period, as Fleischmann had the puck in front of Enroth and used a deft move to get the goalie moving but backhanded the puck off the post.
The Panthers finally beat Enroth at the 8:16 mark, after a weak clearance attempt by Alexander Sulzer. Enroth was slow to get up and Tom Gilbert took a slap shot that Boyes, an ex-Sabre, deflected into the goal.
Florida had another Boyes goal disallowed when play was blown dead due to an injury to defenseman Dmitry Kulikov in the Panthers zone. Kulikov was bleeding after being struck in the face with a high stick.
"Ultimately, Boyes' goal in the period should have counted or there should have been a four-minute penalty, one or the other," Horachek said. "But that's the way it goes. "
Thomas made a sliding stop on Brian Flynn in overtime.
Jonathan Huberdeau appeared to put the Panthers in front during the shootout, but was ruled to have pushed Enroth's pad across the line.
Campbell played in his 800th career NHL game. His first 391 came with Buffalo, which drafted him in the 6th round of the 1997 NHL Draft.
"You want to have longevity in this game and it all started here so it's nice to be back here," Campbell said.
The 34-year-old defenseman said it's weird to see the Sabres with a new general manager, but is hopeful for the team's fan base.
"Hopefully Pat LaFontaine can steer them in the right direction," Campbell said. "I'm sure he will. Hopefully it's good things ahead for the fans. They deserve it. It's been tough sledding. I know we were good in `05 and `06 and got her going but the Bills have struggled a little bit, too. They deserve a lot more for all the support they give."
The Sabres next play in Washington on Sunday, while Florida travels to New Jersey for a Saturday night game.
It was Buffalo's first game since Jan. 4. A blizzard caused the postponement of Tuesday's game against Carolina. ... Florida's scratches were C Scott Gomez, D Mike Mottau and C Shawn Matthias. ... Tyler Myers sat out the first game of a three-game suspension for a hit to the head of Dainius Zubrus.