Jake Sanderson had a goal and an assist, and Batherson scored for the Senators (41-29-6), who have won two straight, and moved within four points of the Panthers for third in the Atlantic Division. Ottawa is also five points ahead of the Montreal Canadiens for the first wild card in the Eastern Conference.
"Tonight, he was an absolute stud," Sanderson said of Forsberg. "They threw every single puck to the net, and honestly, I thought the most impressive part about his game was that he was getting out of his crease, playing the puck very well, and when he does that, it helps the whole team. He was awesome tonight."
Sergei Bobrovsky made 19 saves for Florida (44-28-4), which clinched a berth in the Stanley Cup Playoffs when the Columbus Blue Jackets lost 5-0 against the Toronto Maple Leafs.
"It's definitely frustrating," Panthers forward Jonah Gadjovich said. "Obviously we want to get the wins this time of year but our product is right right now. I think that our game is good. We're playing the right way, we're doing what we want to do, just not getting the final outcome that we want."
Florida, which has lost four straight games (0-3-1), was shut out for the first time since Dec. 18 (4-0 loss to the Canadiens). The Panthers are two points behind the Tampa Bay Lightning for second in the Atlantic and six points behind the first-place Toronto Maple Leafs.
"I feel like 5-on-5 we were the better team," Florida forward Jesper Boqvist said. "We created some really good chances, but I guess we've got to make the goalies make a harder save, right? I mean, a lot of good stuff, but we've got to get those points, I guess. Regroup for tomorrow (at the Detroit Red Wings)."
Sanderson gave the Senators a 1-0 lead at 11:21 of the first period. Shane Pinto circled the Panthers net and found Sanderson in the left slot, who one-timed it over Bobrovsky's right shoulder. Sanderson, who set an NHL career-high in goals with his 11th of the season, has a four-game goal streak at home.
"I think there's certain players that you just kind of sit back and you watch," Ottawa coach Travis Green said of Sanderson. "You don't over coach; you just watch them develop. His game is just slowly evolving into more. It's great to watch and see him progress. We're lucky to have him, quite honestly."