"He made a nice move," Miller said about Booth's goal. "I see him all summer, but I didn't see that one. I was happy to come through later on."
The victory improved Buffalo's record in shootouts this season to 6-2.
"It starts with Ryan making the saves," coach Lindy Ruff said. "You get a big save and get a goal, that pumps Ryan up. When you see him on the road get the first save and you get the next one, that puts a lot of pressure back on the home team. That means they have to get the next two. Ryan's done a good job on the shootout."
Thomas Vanek and Tim Connolly scored in regulation for the Sabres, who have won three in a row and seven of nine.
Horton had the other goal for the Panthers, who haven't lost in regulation in eight games (5-0-3).
Florida dropped to 2-6 in shootouts. Only Tampa Bay (2-7) has lost more this season.
"It's frustrating," Panthers coach Pete DeBoer said. "But what are you going to do about it? We can't practice it any more, we've tried different shooters, both goalies haven't had much luck at it. Hopefully, the tide will turn somehow for us."
Miller finished with 27 saves. Florida's Tomas Vokoun stopped 24 shots.
With Buffalo up 1-0 in the shootout, Roy clinched the victory on the Sabres' second attempt thanks to a little bit of luck. He lost control of the puck as he attempted to deke to his backhand, but it slid between Vokoun's legs.
Kotalik, who is 5-for-8 in shootout attempts, scored with a high backhand off a deke.
"First one I was almost certain I had it," Vokoun said. "Second one, the guy lost the puck. It's tough when he doesn't know what he's doing. It's tough to lose this way."
Florida had the best opportunity in overtime when defenseman Jassen Cullimore grabbed a loose puck in the slot with Miller out of position. But Miller was able to make the save.
Buffalo led 2-1 until Horton tied the game with 3:24 left in the third period thanks to a brilliant play by Richard Zednik, who backhanded a pass between his legs to the front of the net. Horton made a quick move to the forehand to beat Miller.
"At least we're getting the point," Booth said. "We're coming back, down a goal or two late in the game, so that's a positive. Now we've got to get to the next level and start to win those games."
Vanek broke a 1-all tie early in the third on Buffalo's second power play of the third period, with both penalties called on All-Star defenseman Jay Bouwmeester. Vanek scored on his second rebound attempt after Toni Lydman's wrist shot from the point bounced off the chest of Vokoun. The puck bounced off the stick of defenseman Karlis Skrastins before slowly sliding into the net.
Skrastins also had bad luck on Buffalo's first goal, which tied the score at 1 with 1:57 left in the second period.
After Florida center Gregory Campbell grabbed a rebound to the side of the Panthers' net, Connolly hit Campbell's stick and made him lose control of the puck. The puck slid to the front of the net and ricocheted into the net off the right skate of Skrastins.
"You need breaks," Ruff said. "You can miss great opportunities, then bad bounces bite you. You take advantage of them. We found a way to go in. He whacked the stick and you get those when you're going good - and when you're not, none of those go in for you."
Booth opened the scoring 16:29 into the opening period on the first penalty shot of his career. Booth, who was awarded the penalty shot when he was taken down by Lydman, beat Miller with a deke to the forehand.
"Best chance you have to score in a hockey game is 1-on-1 with the goalie," said Booth, whose shootout attempt was his first of the season. "Just made my best move, and I'm just disappointed I didn't have one in the shootout."
Notes: Buffalo began a season-long six-game road trip. ... The Sabres played without defensemen Teppo Numminen (broken jaw) and Andrej Sekera (ankle), both of whom were injured within the last week. Numminen and Sekera will be sidelined indefinitely. ... Florida C Kamil Kreps returned after missing nine games because of a shoulder injury. ... Florida LW Ville Peltonen missed the game because of a knee injury sustained Saturday at Tampa Bay. Peltonen also is expected to miss Wednesday's game against Dallas. ... Booth's goal was the second on a penalty shot for the Panthers this season, matching a franchise high. They also had two in 1998-99 when Ray Whitney and Pavel Bure scored.