The Panthers blew a three-goal first-period lead but hung on to win for the third time in four games.
"We just had to re-focus and play with a little bit more composure," said Higgins, who scored for the first time since Nov. 12. "We handled the puck like a hot potato in the second period but did a much better job of handling their pressure in the third."
It was the second time in the last nine days that Florida had built a 3-0 lead after the first period. But unlike the game against Carolina in which the Hurricanes wound up digging out of the hole to win 4-3, the Panthers were able to withstand Buffalo's blitz to take a 3-3 tie going into the final frame.
"On the road being 0-0 going into the third period, it's not a bad spot to be," captain Bryan McCabe said. "That's what we talked about. They dominated us in the second, but in the third we got the forecheck going again."
Stephen Weiss had a goal and assist and Tomas Vokoun finished with 45 saves for Florida, playing its third game in the past four nights.
Weiss also played a somewhat controversial part on the winning goal as well. While the teams were playing with four skaters each, he appeared to slash Buffalo defenseman Tyler Myers on the ankle, causing Myers to fall and lose control of the puck inside the Florida zone.
Garrison pounced on the loose puck and skated down the right wing before eventually putting a wrist shot past Buffalo goalie Ryan Miller with 5:07 left in regulation.
"I had him beat and he took me down with a trip," Myers said. "If he doesn't take me down, it's a scoring chance for us. I'm pretty upset about that."
Jordan Leopold scored twice and Jason Pominville had a goal and assist for the Sabres, who've dropped three of their last four -- including two to the Panthers over the last six days.
Miller, making his 12th straight start, made 25 saves but was denied in his bid to become the 67th goalie in NHL history to win 200 games.
"We lost the game in the first period. We didn't lose it in the third," Leopold said. "There's no excuse for that."
The Sabres also lost leading scorer Derek Roy just seven minutes into the game after he was driven into the boards by Florida defenseman Dmitry Kulikov while carrying the puck into the Panthers' zone. Roy skated off while favoring his left leg and went directly to the locker room.
Coach Lindy Ruff didn't disclose Roy's injury but added that it "looks serious." Roy was seen leaving the building with crutches and will be re-evaluated on Friday to determine the extent of his injury.
Down 3-0 after the first period, the Sabres tied it with three consecutive goals in the first 12 minutes of the second period.
Leopold scored Buffalo's first goal at 5:44 of the second with a shot from the top of the left circle that trickled past Vokoun.
Pominville made it 3-2 with a power-play goal at 8:15, wristing a shot in from the right faceoff dot.
Leopold then tied it with his second of the period and ninth of the season, splitting the Florida defense at the blue line before putting a wrist shot past Vokoun from the slot 4:06 later.
Higgins gave the Panthers a 1-0 lead just 1:10 into the game, batting home a rebound out of the air after Miller blocked the original shot by Evgeni Dadonov. The goal was upheld after a brief video review confirmed Higgins didn't high-stick the puck in.
Weiss pushed Florida's lead to 2-0 at 12:10 of the opening period while the Panthers enjoyed a two-man advantage. From the right circle he completed a nifty tic-tac-toe passing play that also involved Michael Frolik and McCabe.
Florida made it 3-0 when Higgins notched his second of the game 1:43 later, depositing a backhander in from the lower-right circle.
Leopold became the first Sabres defenseman since Phil Housley in 1989-90 to score nine goals before Jan. 1. Housley had 10 before the New Year and finished with 21 that season. ... The Panthers have outscored the Sabres by a combined 7-0 in the first period of both of the meetings between the two teams this season. ... Buffalo's 20 second-period shots tied a season high. The Sabres also had 20 shots in the third period against the Ottawa Senators on Oct. 22.