Alex DeBrincat, Austin Watson, Brady Tkachuk scored for the Senators, and Tim Stutzle added an empty-net goal.
''It brings a lot of confidence,'' Forsberg said. ''The points haven't gone our way so far so we have to keep building on it, trust the process and trust our game and stick with it no matter what happens and just keep on working.''
Tage Thompson scored for the Sabres, who lost their seventh straight game.
Eric Comrie started in net for Buffalo, but was unable to finish the game after stopping 22 of 24 shots. Craig Anderson, the longtime former Senators goaltender, came in midway through the second period and finished with 14 saves.
''I just tried not to be emotional,'' Anderson said. ''I spent a lot of time here, and seeing some of the memories, it was nice to kind of flash back on. It's in the past. I definitely enjoyed it.''
With a combined 14 minor penalties, it was difficult for either team to generate any real momentum.
Ottawa took five penalties in the first period, but still managed to take a 1-0 lead into the break on Watson's 50th career goal.
''I don't think I've ever killed so many penalties in the first two periods of a game . but credit to our penalty killers starting with (Forsberg), who made some awesome saves,'' Watson said. ''Killing a couple off there early kind of gave us our mojo a little bit on the kill.
''That special teams battle is often times the difference in the game.''
The Sabres went 1 for 8 with the man advantage and had a total of six shots on the power play.
''Our power play didn't look good tonight,'' Sabres coach Don Granato said. ''Even after the entry, we hurried things, we forced things, we went individual too quickly. That's something we have to take a quick look at.''
Trailing 2-1 to start the third, Buffalo pushed for the equalizer with JJ Peterka hitting the crossbar early in the period. But, DeBrincat made it 3-1 at 14:21 into the period with his fifth of the season.
With plenty of missed chances, Buffalo knows it needs to keep things simple and not get up in the losses as the team tries to turn things around.
''I think we're gripping the stick too much,'' defenseman Rasmus Dahlin said. ''We have our chances, but we can't really execute right now. We need more swagger to our game. I don't know how many chances, but we had a ton today.''
After going 0 for 5 on the power play in the first period, the Sabres capitalized and scored their sixth power play to tie the game 1-1. Thompson fired a shot from the faceoff circle for his team-leading 12th goal of the season 6:41 into the second.
The Senators regained the lead just over three minutes later when Tkachuk put a backhanded shot past Comrie on the power play.
Moments before the goal, Comrie had a collision with Ottawa's Mathieu Joseph. He remained in goal, but was eventually replaced by Anderson.
It was Craig Anderson's first time back at Canadian Tire Centre since leaving as an unrestricted free agent in 2020. Anderson holds the Senators franchise record for most regular-season wins (202) and games played (435) by a goaltender.
Buffalo: At Toronto on Saturday in the second game of a three-game trip.
Ottawa: Host New Jersey Devils on Saturday in the finale of a three-game homestand.
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