Tonawanda News — Stamkos extended his goal-scoring streak to six games with his 14th.
"We had a lot of good chances, and their goalie played well," said Stamkos, who had eight shots.
Stamkos put the Lightning up 1-0 at 1:24 of the first on a rebound goal from the slot after Miller made a save on Teddy Purcell's shot.
Hodgson tied it at 1 with 9:58 left in first from behind the net when his pass toward the slot deflected off a Tampa Bay defender and past goalie Mathieu Garon.
"Obviously, it's frustrating, but we did enough things to win," Tampa Bay defenseman Victor Hedman said.
Garon stopped 19 shots.
Buffalo had lost in four in a row, including two under Rolston.
"It was good for all of our guys to sit in that room and have that feeling where they did a lot of things right tonight and got rewarded for it," Rolston said.
Lightning defenseman Sami Salo left in the second with an undisclosed lower-body injury. Tampa Bay coach Guy Boucher said he didn't know how long Salo will be sidelined.
"It was a tough game," Boucher said. "We lost a defenseman. We got beat by a goaltender."
NOTES: Tampa Bay C Cory Conacher had an assist, giving the rookie four assists and six points during a six-game point streak. ... Vanek has 12 assists and 35 points in 29 games against Tampa Bay. ... Lightning LW Ryan Malone, who has sat out nine straight games with an undisclosed lower-body injury, is skating in practice. ... Sabres D Jordan Leopold missed his third consecutive game because of an undisclosed upper-body injury.