Victor Olofsson scored two goals, Robert Hagg had a goal and an assist, and Tage Thompson had two assists for the Sabres (4-1-1), who had lost their previous seven games to the Lightning dating to Nov. 13, 2018.
"That's the reigning Stanley Cup champs. That's a great hockey team over there," Anderson said. "I think our guys showed up ready to play, put the work boots on and tried to frustrate them by outworking them. Any time you win, it's satisfying. This is a tough league to play in, it's a tough league to get wins in. Kudos to our guys for putting in the work tonight."
Alex Killorn scored, and Brian Elliott made 20 saves in his season debut for the Lightning (2-3-1), who are 0-2-1 in their past three games.
"We shouldn't be frustrated. It's a 1-1 game and I felt we pretty much had the puck all night," Tampa Bay coach Jon Cooper said. "But you can't feel good about yourself no matter who you are playing or how the game is. You just take a look at the second goal that was scored and how we played that. We changed the way we played. We changed our mindset. And any time you are going to turn the puck over in the NHL, you are just flirting with fire. And we did that. And obviously, that (second) goal was a killer for us."
Olofsson gave Buffalo a 1-0 lead at 1:41 of the first period, shooting into an open net from the right circle after Elliott gave up a big rebound on Thompson's initial shot.
Tampa Bay has allowed the first goal in each of its six games this season.
Killorn tied it 1-1 at 18:26 of the first when he got his stick on Ryan McDonagh's point shot, causing the puck to trickle through Anderson's pads.
Steven Stamkos nearly gave the Lightning the lead at 18:14 of the second period. He skated in on a breakaway, but Sabres defenseman Mark Pysyk recovered on the backcheck and lifted Stamkos' stick before he could attempt a shot.
Shortly after, Drake Caggiula held off Tampa Bay defenseman Mikhail Sergachev and scored on his own breakaway to give Buffalo a 2-1 lead at 19:22.