The victory completed a 4-0 homestand for the Panthers and gave them their first four-game winning streak since March 2008.
"That's unbelievable," veteran center John Madden said. "You play a lot of games and you just think you can get something. But that's good on us. A lot of guys in here are playing a little banged up, but they battled through it. It's fun to be invested in this dressing room."
The Panthers have won five in a row at home overall, tying a franchise record last accomplished in 2010.
More important is that the Panthers increased their lead in the Southeast Division to five points over Washington and to seven points over Winnipeg, with each team having 11 games remaining.
"Right time to do it," Madden said. "We're starting to hit our stride. I've been on plenty of teams heading into the playoffs and it's really crucial to be playing good hockey going into the playoffs, not limping into the playoffs."
Kulikov, who had been 1-for-2 in shootouts this season, beat Ryan Miller with a deke to the backhand.
"He was a little deep in the batting order but sometimes you're looking for a little swagger and Kuli is a cool cat, not a whole lot ruffles him," Panthers coach Kevin Dineen said. "He's had a long stretch off and we wanted to get him and (Kris) Versteeg on the ice early. They started the game and a pretty good way to finish, scoring the big goal for us."
For Kulikov, who hadn't played since undergoing knee surgery on Jan. 24, the game ended a lot better than it started.
"To be honest, it was pretty rough out there," Kulikov said. "I didn't feel very good in the first period, it felt like guys were just flying around and I was just standing there. It got better, I picked up the tempo a bit. I feel pretty good about myself today."
Theodore also was feeling great after he stopped Stafford in the shootout. He immediately threw his arms in the air, looked at the Panthers' bench and began pumping his arms in celebration.
As Theodore's teammates rushed to congratulate him, plastic rats began raining down from the stands.
"Both teams wanted the points and needed the points," Theodore said. "I'm sure Buffalo is happy with the one point. The extra point is huge right now."
Wojtek Wolski also scored in the shootout for Florida, while Tyler Ennis answered Wolski's goal on the back end of the second round.
By going last in the shootout, Buffalo had four chances to win before Kulikov scored. Theodore stopped all four shots, sending the Sabres home with a single point.
"Any point you lose right now is a lot," Sabres coach Lindy Ruff said. "If it was a half a point it would be a lot. We've got to move on to the next game and try to get two. It's disappointing. The points in the shootout are big points. I picked one good shooter and six bad ones tonight."
Florida improved to 5-8 in shootouts, while Buffalo dropped to 7-6.
With the one point, the Sabres moved into a tie with Winnipeg for ninth place in the Eastern Conference. Both teams are two points behind eighth-place Washington, although the Sabres have played one more game than either the Capitals or Jets -- both of whom play Sunday.
But the Sabres also continue to waste great opportunities. Buffalo has been tied after two periods in its last seven games but has gone only 3-2-2 during that stretch.
"We gave away a point (Wednesday) and felt like we gave one away tonight, so it's basically a loss," Miller said. "We're not making up any ground here."
It was a difficult loss for the Sabres, who outplayed the Panthers for large chunks of the game.
Florida didn't manage a shot on goal in the first 17 minutes of the first period, was held to one shot in all of the third, and there were no shots by either team in an overtime period that featured not a single stoppage of play.
"I think we played a pretty solid game," Buffalo captain Jason Pominville said. "We worked hard, we generated some opportunities. If we work as hard as we did tonight, on most nights we'll be able to put some away."
Despite ending up with only four shots in the first period, the Panthers led 2-1 thanks to goals by Mikael Samuelsson and Madden 38 seconds apart. The goals came on Florida's first two shots.
"Not every game is going to go as drawn up," Madden said. "You've got to find ways to win and obviously Theo played a big part in our win tonight. We scrambled in front of the net a few times. Sometimes the shot clock doesn't always show the truth, we had the zone time, we passed up some shots for whatever reason. They did a good job blocking, too. You've got to give them some credit and take the good out of this game and keep moving forward."
Ennis and Derek Roy scored for Buffalo, which lost for only the fifth time in 14 games (9-2-3).
Miller made 15 saves as Florida finished with a season-low 17 shots.
The Florida victory evened the season series at two victories apiece.
Bidding to earn a playoff spot for the first time since 2000, the Panthers welcomed two key regulars to the lineup — Kulikov and Versteeg, who had missed the previous nine games with a lower-body injury.
Buffalo's Andrej Sekera returned to the lineup after missing five games with pneumonia, but fellow defenseman Tyler Myers sat out the second game of a three-game suspension for boarding Montreal's Scott Gomez on Monday.
Ennis opened the scoring just 1:15 after the opening faceoff when he one-timed Stafford's pass from behind the net. Ennis didn't hit the puck cleanly and it slid slowly between Theodore's legs.
The goal gave Ennis four goals and seven points in his last four games. Marcus Foligno had the second assist on the goal, giving him five points in four games since being recalled from the AHL on March 9.
Samuelsson scored at 17:15, getting his second power-play goal in two games with a one-timer from the high slot. The shot beat Miller high to the stick side.
Madden gave Florida the lead at 17:53 with his second goal in two games after he went scoreless in his first 19 games with the Panthers. Madden skated down the left wing on a 2-on-2 rush and beat Miller with a low wrist shot to the short side.
"We only gave them two (chances) and both of theirs went in, and one of our six or seven went in," Ruff said. "Give a lot of credit to Theodore, he made some good saves. We had four opportunities in the shootout to put it away, too, and didn't put it away. We have nobody to blame for ourselves."
Roy scored the only goal of the second period on the power play at 9:41. After cleanly beating Jerred Smithson on the faceoff, Roy grabbed a long rebound off Pominville's shot from the point and beat Theodore with a high backhand.
There would be no more scoring until the shootout, and Kulikov was only too happy to get a shot.
"Whatever coach asks me to do, I'll do," he said. "If he asked me to go out there and be a goalie ... No pressure on me. Pressure on the whole team. I made the goal and we have confidence in Theo. I was hoping he would make that save."
Said Dineen: "You can't do any better than winning them all. Tonight was emotional, playing against a desperate hockey team, and to get the win in a shootout is something that hasn't been our specialty this year."
1 - 0 BUF
1 - 1 Tie