Clemmensen helped the Panthers win despite being outshot 41-17.
"I think we're all really happy with Clem's game tonight, including his teammates," Panthers coach Kevin Dineen said. "It's one of those ones where he was a difference-maker. They put a lot of pressure on us and we were able to withstand it and find a way to win."
Clemmensen, who watched top prospect Jacob Markstrom start Florida's previous six games, got his first victory in more than a month. He had lost his past five decisions since a 6-4 victory against the Pittsburgh Penguins on Feb. 26.
"It's been a long time since my last win, unfortunately," Clemmensen said. "It's a good feeling to win. It's not easy going long stretches between games, but it's a situation I've been in in the past many times and experience helps you a little bit. All in all, it was just a matter of getting those first couple of saves and going from there."
Clemmensen came into the game with the worst GAA (3.96) and save percentage (.862) among NHL goalies with at least 10 appearances this season, but he was brilliant from the start against Ottawa.
He stopped all 30 shots he faced over the last two periods.
"I thought we played great really the whole night," Senators coach Paul MacLean said. "I thought we dominated the game for the most part but we got goalied. We've done that to other teams in the past. For us, the good sign is we played hard for the 60 minutes and we created opportunities. We just have to find a way to get more pucks on to the net on our power play and compete for the opportunity to score a little more than we have."
The Senators have lost four straight to match their longest streak of the season. Ottawa missed a chance to tie the Toronto Maple Leafs for fifth place in the Eastern Conference standings and are two points ahead of the New York Rangers and New York Islanders.
"We realize what's going on," Senators forward Kyle Turris said. "We haven't won in four straight and there's a big 10 games left in the season. We have 10 games to turn things around and play our game. We're confident we'll do that."
Clemmensen's most spectacular save came in the last five minutes of the second period when he stuck out his pad as he was falling and kicked out Turris' point-blank shot as the puck was reaching the goal line. It was a close enough call that the play was reviewed.
"For some reason my weight was not on the correct side, so I ended up kind of falling over," Clemmensen said. "It was probably a save that I shouldn't have had to have made in that fashion. You've got to be lucky to be good sometimes, but it probably shouldn't have been that type of save in that situation. Regardless, it kept the puck out."
Anderson, who came in with the best goals-against average and save percentage in the NHL, made 15 saves in his first appearance after missing 19 games with an ankle injury.
"I stood around a lot," Anderson said. "Had to skate around a lot to try and stay warm and stay focused. Sometimes those are the hardest games to stay mentally in the game."
When MacLean gave his players the day off on Saturday, Anderson spent it at his home in Coral Springs, Fla.
Anderson spent three years as the backup to Tomas Vokoun with the Panthers from 2007-09 and came into the game Sunday with a 9-0-1 record in 11 career appearances against his former team.
"That's one of those stats that you flip through the game notes before and that one sticks out," Dineen said. "Don't discount that he's got a home here, he works out here, he's got a quality fan base and friend base that's based out of here. So good for him, but even better for us to pop that bubble."
The victory was the Panthers' first this season against the Senators in three tries, and their second in the past 12 meetings.
Marcel Goc also scored for the Panthers, who have the worst record in the Eastern Conference but have won four of five.
Cory Conacher scored his first for the Senators after he was acquired at the NHL Trade Deadline in the deal that sent goalie Ben Bishop to the Tampa Bay Lightning. Conacher is second among NHL rookie scorers, two points behind Florida's Jonathan Huberdeau, who had an assist on the game-winning goal.
Kulikov scored on Florida's only power play of the game. With Sergei Gonchar in the box for holding, Kulikov fired a wrist shot from the high slot that went through Ottawa forward Zack Smith and beat Anderson on the blocker side.
Kulikov's goal was his second of the season, each a game-winner, the other coming March 30 in overtime against the New Jersey Devils.
It was the fifth consecutive game with a power-play goal for the Panthers. They are 12-3-1 this season when they score at least one power-play goal, 1-17-5 when they don't.
Ottawa was 0-for-5 on the power play, making the Senators 0-for-17 in their past four games.
Conacher opened the scoring at 12:26 of the first period after Mika Zibanejad fed Jakob Silfverberg in the slot. Instead of shooting, Silfverberg slipped a pass across the crease to Conacher for the easy tap-in.
"Obviously, it would be a little better to celebrate with a win," Conacher said. "I have to give so much credit to the two guys I played with. They made good plays on that play. I basically just had to finish it off and tap it in."
Goc tied the game 1:08 into the second period when he tipped Tomas Fleischmann's wrist shot from the top of the left circle.
Sunday, though, was all about Clemmensen.
"I thought overall as a team we played a pretty good game," Anderson said. "We had momentum for most of the game and we put a lot of pucks at the net. It was one of those nights we ran into a hot goaltender.
"Give Scott credit where credit is due. He made some big saves and stole them the game."