Kulikov scored at 1:43 of overtime and the Panthers beat the New Jersey Devils 3-2 on Saturday.
Kulikov's shot from the right circle beat Martin Brodeur on the far side.
"It's good to get (that first goal) out of the way, and especially to get a win for the team it's even better," Kulikov said. "It's special to win a game in overtime, regardless."
The Panthers have won two in a row at home for the first time this season. They beat the Buffalo Sabres in a 5-4 shootout win on Thursday.
"That was a full team effort tonight," Panthers coach Kevin Dineen said. "I felt there was a lot of belief on our bench (after that Steve Bernier) goal. We kept putting pucks on net, and when you do that good things happen. It was an entertaining game; the last two have been entertaining games for our team and our fans."
Bernier scored two goals for the Devils and Brodeur stopped 27 shots. The Devils have lost three straight.
Matthias' second goal tied the game at 2 with 27 seconds left in regulation. He grabbed a rebound in front of the crease and wristed it past Brodeur.
Matthias has a career-high 14 goals and 11 in the past 16 games. Matthias also had two goals in Thursday's win over Buffalo.
"I've had my opportunities here, and it's up to me to take advantage of it. It feels good to capitalize on it," Matthias said. "It feels good getting that (goal) and getting that win."
Tied at 1, Bernier scored his second goal at 7:57 of the third on a power play. Henrik Tallinder took a shot from the high slot and Bernier deflected it into the net to give the Devils a 2-1 lead.
Bernier hadn't scored a goal since March 2 at Buffalo and this was his first multi-goal game since Feb. 3 at the New York Islanders.
But the Devils couldn't hold the lead and lost past regulation for the third straight game.
"It's better than no points. But all in those games we were ahead in the third period," Bernier said.
The Devils blew a two-goal lead on Friday night's 5-4 shootout loss at Tampa Bay, with the tying goal coming with 15.1 seconds left.
"They hurt. We've got to figure out a way to close these games, that's the bottom line," Devils coach Peter DeBoer said. "We're leaving some points on the table. You hope it doesn't come back to haunt you."
The Devils took a 1-0 lead on Bernier's first goal. The Panthers turned the puck over on a pass from behind the net and Bernier backhanded in a pass from Ryan Carter at 3:42 of the first.
The Panthers tied it at 1 on a power-play goal by Matthias. Jonathan Huberdeau took a shot from the right circle and Matthias deflected it in at 12:55.
"It's unfortunate that we're not able to close out games," Brodeur said. "Both times with less than 30 seconds and we can't get it done, and after that we don't win in overtime or the shootout. It's disappointing, but we keep getting points and that's the only thing positive about it."
Panthers RW George Parros returned from an upper-body injury. ... Panthers F Greg Rallo was reassigned to AHL San Antonio. ... The previous time the Devils visited the Panthers they eliminated them from the opening round of the playoffs with a 3-2 double-overtime win in Game 7.