Rasmus Dahlin had a goal and two assists, Zach Metsa tallied a goal and an assist, and Ukko-Pekka Luukkonen made 36 saves for the Sabres (35-19-6), who beat the Florida Panthers 3-2 on Friday night and have won three straight.
Dominic James and Victor Hedman scored for the Lightning (38-16-4), who have lost two in a row after winning their previous six games. Andrei Vasilevskiy gave up five goals on 14 shots before he was pulled at 1:54 of the second period in favor of Jonas Johansson, who made 20 saves in relief.
Dahlin gave Buffalo a 1-0 lead at 5:25 of the first period when he took control of the puck and skated to the middle of the ice where he notched a wrist shot that beat Vasilevskiy to the far post.
Just 50 seconds later, Norris pushed it 2-0 at 6:15 when he took a pass from Josh Doan at the right circle and faked a cross-ice pass before beating Vasilevskiy with a shot to the far post.
The Sabres extended the lead to 3-0 at 8:18 with Norris' second goal, a redirection from in front of the net off a slap shot from Bowen Byram.
Tage Thompson made it 4-0 at 15:06 when he took a backhand pass from Peyton Krebs and scored on the forehand from close range.
Metsa pushed the Buffalo lead to 5-0 at 1:54 of the second period after he intercepted a clearing attempt by Lightning forward Anthony Cirelli and scored on a shot from above the hashmarks that beat Vasilevskiy on the stick side.
James put the Lightning on the board 5-1 at 16:03. Mattias Samuelsson's clearing attempt off the left boards was intercepted by Hedman, who passed to Bjorkstrand in the slot before the feed to James, who beat his man out of the corner to get the wrist shot off.
Alex Tuch made it 6-1 at 3:43 of the third period with a wrist shot from the point with center Ryan McLeod providing the screen in front of Johansson.
Hedman made it 6-2 at 5:27 with his first goal of the season, a slap shot from above the left circle.
James exited the game with 2:48 left following a hit from Michael Kesselring against the boards, who was issued a cross-checking penalty for the hit.
