Kulikov and Garrison scored first-period goals, Scott Clemmensen stopped 25 shots for his seventh career shutout, and the Panthers routed the Dallas Stars 6-0 on Tuesday night.
Florida started the night leading the league in points from defensemen. Assists from Brian Campbell and Mike Weaver made it a four-point night for Florida's defensemen, giving the Panthers 52 points from their D this season.
"It's definitely a mentality," Garrison said. "The forwards work hard down low, we work low to high and get shots through. That's definitely the game plan."
Evgeny Dadonov also scored for the Panthers.
Weiss skated in his 574th game for the Panthers, breaking a tie with Robert Svehla and moving into second place on the franchise list behind current Dallas Star Radek Dvorak's 613 games.
Clemmensen was also on top of his game against a team that started the night second in the Western Conference with 22 points.
"It's a team effort," said Clemmensen, who missed 13 games this season with a knee injury.
"Everybody contributed. It's a lot of fun to be a part of it. You play good defense, score some goals from the blue line, that's a good combination."
The Stars, coming off consecutive road losses to Pittsburgh and Detroit, had been 6-1 at home. Dallas, which has lost a season high three in a row, opened a stretch of five of six games at home with its most lopsided defeat of the season.
"This is probably the most embarrassing game we've had at home in quite some time, this season anyway," Stars captain Brenden Morrow said.
"Right now, you look back, it's probably been about nine periods where we've been outworked. Some periods in there, 5 to 10 minutes in those games where we've done things well, but it's pretty simple, we got outworked these last few games."
Kari Lehtonen kept the Stars in the game early with a series of tough saves before the Panthers scored.
Kulikov connected from the slot off Tomas Kopecky's centering pass at 16:44 of the opening period. It was Kulikov's first goal of the season.
Garrison beat Lehtonen for his seventh goal of the season to make it 2-0 at 18:08 of the first period.
Florida held a 14-4 shots edge in the first 20 minutes and didn't let up.
Fleischmann fired into the top right corner of the net from the slot for his seventh of the season at 15:02 of the second. And Weiss made it 4-0 with 7.6 seconds left in the second for his sixth goal of the season.
Versteeg's ninth goal of the season halfway through the final period gave the Panthers a five-goal edge, and Dadonov completed the scoring at 13:19 when the puck went in off his skate for his second of the season.
The Stars are facing their first adversity of the season after getting off to a fast start.
"I just think the honeymoon's over," rookie coach Glen Gulutzan said. "You start off 11-3 and teams are prepared to play you, they probably watch you a little closer and I thought Florida did a really good job pre-scouting us."
Notes: The Panthers are 7-3 on the road, 2-2-3 at home. ... The Stars placed D Alex Goligoski on injured reserve with a broken thumb four days after he was injured in a 3-1 loss at Pittsburgh, his former team. Goligoski is second among Dallas defensemen with six points, including two goals. Goligoski could be out for as long as a month. ... Stars second-line LW Steve Ott sat out his sixth straight game with a hip pointer. ...The Panthers are 11-11-3 all time against the Stars. ... Forwards Scottie Upshall, Jack Skille and Mikael Samuelsson are all out for Florida with lower-body injuries.