"We were just rolling," Tampa Bay coach Jon Cooper said.
Radko Gudas, Brenden Morrow, Jason Garrison and Brett Connolly had the other Tampa Bay goals. The Eastern Conference-leading Lightning improved to 5-0-1 in the last six games, with lone loss in a 2-1 shootout defeat at Buffalo on Tuesday.
Buffalo, which had won six of seven, went 22 1/2 minutes without a shot during one stretch before Rasmus Ristolainen got one with 3:41 left in the second.
"We just lost track of what we have to do in order to be successful," Sabres coach Ted Nolan said. "We stopped hitting, we stopped skating, just doing a lot of pirouettes in center ice, and it got away from us in that second period."
The Sabres, last in the Atlantic Division, are 1-13-1 when the opponent scores first, and are pointless when trailing after the first (0-10-0) and second (0-12-0) periods.
After Stamkos was left alone near the post and scored his 16th goal of the season off a pass from Ryan Callahan at 4:28 of the second, Morrow made it 3-0 from in-close 71 seconds later.
The Lightning went up 4-0 on Garrison's goal with 6:20 left in the period.
"It was a good team win," Bishop said. "A full 60 minutes."
Gudas opened the scoring 2:33 into the game when his long-range shot got past Jhonas Enroth.
Enroth was credited with a save on Tyler Johnson's shot during a 2-on-none that hit the post in the final minute of the first. He finished with 30 saves.
There were three scrums through the midway point of the third that resulted in four fighting majors and six 10-minute misconducts. Stamkos was given minor penalties for slashing and roughing during the first.
"At least we showed some fight in the third," Nolan said. "The first was OK and the second was awful. In the third, at least we battled back a little."
Connolly had a late third-period power-play goal. Stamkos got his second assist of the game on it.
NOTES: Bishop is 5-0-1 against the Sabres. ... This was Bishop's first shutout this season and ninth overall. ... Buffalo C Cody McCormick was back in the lineup after missing four games with a concussion. ... Tampa Bay C Tyler Johnson had an assist to extend his point streak to five games (five assists, seven points). .... Sabres RW Drew Stafford missed his third game due to a lower body injury but could be back this weekend. ... Buffalo D Tyson Strachan was minus-4. ... There was a video tribute and a moment of silence before the game for Montreal great Jean Beliveau, who died this week.