Killorn led the way with two goals and assist. Johnson also had three points, with his goal ending a five-game goalless drought.
The win gives Tampa Bay a sweep of the regular season series versus the Sabres and marks their 12th-straight win over Atlantic Division teams this season.
The Bolts resume the road trip on Thursday night against the Canadiens in Montreal.
Scoring Summary
1st Period
TBL | 19:03 Conor Sheary (6) - Curtis Lazar
2nd Period
BUF | 2:12 Marcus Johansson (6) - Conor Sheary, Marco Scandella
TBL | 7:00 Ondrej Palat (12) - Tyler Johnson, Mikhail Sergachev - PPG
BUF | 8:12 Jimmy Vesey (5) - Marcus Johansson, Conor Sheary
BUF | 9:56 Jack Eichel (25) - Unassisted - SHG
TBL | 13:57 Alex Killorn (14) - Brayden Point, Nikita Kucherov - PPG
TBL | 16:55 Tyler Johnson (8) - Carter Verhaeghe, Ryan McDonagh
3rd Period
TBL | 6:20 Kevin Shattenkirk (6) - Tyler Johnson, Anthony Cirelli
TBL | 8:08 Alex Killorn (15) - Pat Maroon, Cedric Paquette
TBL | 19:57 Anthony Cirelli (9) - Alex Killorn, Steven Stamkos - EN