It was the first game for the Lightning without captain Martin St. Louis, who was traded Wednesday to the New York Rangers. Forward Ryan Callahan, obtained in the trade, made his Lightning debut, and center Steven Stamkos returned after missing 45 games with a broken right tibia.
Stamkos, appointed captain earlier in the day, will have to wait a bit longer for his first "W" wearing the "C."
"It's tough, you've got a team in here who is not necessarily going to be in the [Stanley Cup Playoffs], and they battle hard and their goalie plays well," Stamkos said. "We can't afford to let teams come in here and beat us down the stretch."
Stamkos played 21:03; he finished with four shots on goal, was credited with two hits and engaged in a prolonged shoving match with Buffalo's Mike Weber in front of the net.
Stamkos showed some rust; he was alone with the puck in front of Enroth with 20 seconds remaining in the second period, deked twice, but couldn't get the puck past him.
"I thought [Stamkos] was outstanding," Lightning coach Jon Cooper said. "If that's the worst game he plays for us, then things are going to look good, because I thought he was the most dangerous player on the ice."
Callahan had four shots and four hits in 16:33 of ice time.
"I thought Callahan was good," Cooper said. "He was good on the penalty kill, he hit guys, and he was in front of the net all the time when we needed him."
Tyler Myers, Cody Hodgson and Marcus Foligno each contributed a goal and an assist for the Sabres, who are 4-1-0 since the Olympic break. Enroth won for the third time in four consecutive starts taking over for Ryan Miller, who was traded to the St. Louis Blues last Friday.
"Goaltending is 90 percent of this game, and when you get good goaltending you have a chance to win," Buffalo coach Ted Nolan said. "We were very opportunistic with our chances. I thought Marcus Foligno played a great game for us, but Jhonas was the backbone for sure."
Myers opened the scoring when he skated the puck into the Lightning end, faked a pass and sent a shot past Lightning goalie Anders Lindback from the left circle. The unassisted goal came at 15:56 of the first period.
Buffalo (19-35-8) upped its advantage to 2-0 on Foligno's seventh goal of the season at 9:25 of the second period. As a loose puck slid across the goal crease, Foligno came from behind the net to score.
Hodgson made it 3-0 with 6:16 left in regulation when Foligno set him up alone in front of the net with a cross-ice pass for his 16th goal of the season
"Marcus really made the play," Hodgson said. "All I had to do was score on a breakaway."
Tyler Johnson scored shorthanded for Tampa Bay, his 19th goal of the season, with 2:29 left to spoil Enroth's shutout.
Tampa Bay outshot the Sabres 44-21, but Enroth was on his game, stopping Ondrej Palat from in front of the net in the first period and poke-checking the puck off Nikita Kucherov's stick as he broke in alone early in the third.
"They had  shots more than we had, so I'd say we were outplayed, but it was a pretty solid road game," Enroth said. "We got the shots from the outside and got a couple of key blocks when we needed them."
The Sabres dominated in blocked shots, 21-6.
It was Buffalo's first win in three tries against Tampa Bay this season. It was the first of a six-game homestand for the Lightning (34-24-5), who are 1-4-0 in their past five.
"Here's the deal," Cooper said. "This is obviously the biggest rut we have been in all year. We've hit a rut. At some point most teams go through these. Sometimes you play pretty well and maybe deserve a different fate, but if you continue to play well you'll come out of the rut.
"I liked the way we played. I didn't like the result. Unfortunately the clock is ticking down on the season and we have to get points."