The Lightning are 3-0-1 in their past four road games and are enjoying their best stretch of the season.
"That's what killed us at the beginning of the year," Stamkos said of a team that was 6-16-3 away from Tampa Bay through Jan. 13. "We know how well we play at home. We needed to prove to ourselves that we could win on the road, as well."
Stamkos scored his NHL-leading 37th goal and extended his point streak to six games, in which he has five goals and five assists. He also set up Steve Downie's goal as part of a two-goal second period. Garon did the rest, stopping 26 shots -- including 13 of 14 in the final period.
The Lightning improved to 9-16-4 on the road, which has helped them go 7-1-2 in their past 10 games.
With 54 points, Tampa Bay (24-24-6) caught the Sabres (24-25-6) and New York Islanders for 12th place in the Eastern Conference. The Lightning beat a team that had been 5-0-1, and hadn't lost at home in regulation in 10 games (6-0-4).
Jason Pominville scored 7:07 into the third period for the Sabres, who came out flat. They managed just 13 shots through 40 minutes while playing for the third time in four nights.
The Sabres failed to build off the momentum of a 3-2 shootout victory over Dallas on Friday, when they rallied from a two-goal, third-period deficit.
"We played one period, but one period is not good enough," Sabres coach Lindy Ruff said. "I was glad to see at least we came out in the third with some determination to try to make a difference."
Determination wasn't enough to beat Garon or the crossbar.
The goalie's best save came with just under 5 minutes left. He slid across the crease in time to get his pad and stick down to stop Pominville's one-timer from the right circle.
Garon also got a lucky break with a minute left when Sabres defenseman Christian Ehrhoff had the goalie beat with a blast from the top of the right circle, only to have the shot clang off the bar.
"That's probably as good of a look as you can have," Ehrhoff said of his shot. "I was going high blocker, and it missed by an inch."
Whew, said Garon, with a big smile.
"The sound is good. The fact that the puck didn't go in after was even better," Garon said. "He just shot a rocket. It was a great shot. He just missed by a little bit. For me, it was obviously a good sound."
Downie opened the scoring 7:31 into the second period, shortly after Sabres goalie Ryan Miller stopped Stamkos' shot from the right circle.
Stamkos then got the insurance goal six minutes later by completing a 2-on-1 break. He was set up by Teddy Purcell, who capitalized on a Sabres turnover in the neutral zone. Driving up the right wing, Purcell fed a pass across to Stamkos, who got off a one-timer as he was falling, and beat Miller just inside the left post.
It turned out to be Stamkos' eighth game-winning goal this season, tying the franchise record he set last year.
Stamkos reserved the credit to Garon, who improved to 6-0-2 in his past eight starts -- a stretch in which he's allowed 19 goals.
"He was unbelievable. He's a big part of why we won," Stamkos said. "We got lucky with the crossbar, but we hit one, as well. It was two big points."
Lightning D Matt Gilroy didn't return after sustaining an undisclosed upper body injury in the second period. ... With Sabres C Cody McCormick out with an upper body injury sustained Friday, rookie forward Zack Kassian played after being recalled from AHL Rochester for a third time this season. The Sabres also loaned rookie C Luke Adam and rookie D T.J. Brennan to Rochester. ... Lightning LW Ryan Malone has begun practicing and is day to day. He has missed seven games with an upper body injury. ... Ruff spent his third game watching from the press box since breaking three ribs in a collision during practice Monday. With assistant James Patrick running the bench, Ruff was healthy enough to ride down the elevator between periods for the first time.
Copyright by STATS LLC and The Associated Press
Arena: First Niagara Center Location: Buffalo, New York
Referees: Dennis LaRue, Ian Walsh Linesmen: Steve Barton, Matt MacPherson
Attendance: 18,690 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Steve Downie (9)
Assists: Victor Hedman, Steven Stamkos
Steven Stamkos (37)
Assist: Teddy Purcell
Jason Pominville (20)
Assists: Thomas Vanek, Mike Weber