The Panthers, who lost 2-1 at Los Angeles on Thursday night, finished 2-2-0 on their four-game road trip.
"We would have liked to have found a way to get a point in L.A.," Florida coach Kevin Dineen said. "At the end of the day, we just beat a really solid hockey team. I think there's really a lot of belief in our locker room right now. Two games now, we got down a goal in the first two minutes and we readjusted from there. It was a really solid all-around effort from our special teams to our goaltending. It was a good hockey game."
The Panthers won their fourth in a row against the Sharks after San Jose went 7-0-1 in the previous eight meetings.
Couture's power-play goal at 13:39 of the third cut Florida's lead to 4-3. Taking a pass from Martin Havlat in the low slot, Couture unloaded, beating Clemmensen to his glove side. But Kulikov scored a power-play goal with 1:35 left to wrap up the win.
The Panthers trailed 2-1 after the first period despite outshooting San Jose 12-8, but they scored three times – each after a Sharks giveaway -- in a hard-hitting second period to take a 4-2 lead.
"I think we gave them that game," Sharks defenseman Dan Boyle said. "A couple of soft plays from us 'D.' Just bonehead stupid soft … soft stupid plays. We gave them a couple of goals. We gave the game away. Their third and fourth goals were both the result of stupid plays, soft plays, dumb plays, and it really (stinks)."
Sturm, a former Shark facing his old team as a Panther for the first time, knotted the score 2-2 at 5:37 of the second. Sharks defenseman Colin White, playing for the first time since Nov. 20, turned it over, and Sturm made him pay, blasting the puck through Greiss' legs and into the net for his second goal of the season.
"That's a big goal for him," Skille said. "It was a great goal, dropping that shoulder and driving the net, tucking it between his legs. I wasn't sure it went in at first. It was good to see. Any time you see a guy that works that hard score a goal, it's always fun to watch."
Fleishmann put the Panthers ahead at 7:15 after a turnover by Sharks defenseman Brent Burns along the boards in San Jose's zone. Versteeg tracked down the puck and feathered a pass ahead to Fleishmann, who cut to his left and put the puck past Greiss.
Sharks coach Todd McLellan was extremely unhappy with the play of his defense.
"We were very sloppy," McLellan said. "That is probably as poorly as I've seen our six 'D' play in four years, altogether as in turnovers. The forwards did not create much of a forecheck. So it was a full team game. We didn't want to work tonight, and we will find some time tomorrow to do it."
Florida made it 4-2 at 18:09 when Skille scored a shorthanded goal. This time Boyle turned the puck over near his own blue line, and Skille made a rush toward Greiss, shooting from close range. Greiss poked the shot away, but the puck hit Boyle's stick, which was on the ice, and bounced into the net.
"What happened was I was just chasing him on his breakout there on the power play," Skille said. "He tried making a pass to the middle, and I was lucky my stick was there. I just thought I had a step on him. ... I just drove it to the far post. I little puck luck at the end helps."
Florida outshot San Jose 15-9 in the second period as they roared back from a one-goal deficit to build their two-goal lead.
"This team's been this way the whole season," Clemmensen said. "We never feel like we're down. We never get down or ourselves or each other. We have a lot of confidence as a team. One-, two-, three-goal deficits, this team battles all the way to the end. You never count us out."
The Sharks built a 2-1 lead in the first period, scoring more than one goal in an opening period for the first time since their season-opener against Phoenix.
Couture gave the Sharks the lead just 1:16 into the game with a highlight-reel goal that seemed to catch the Panthers off-guard. Couture got the puck in the left circle and started skating toward the blue line. He appeared to be looking for somewhere to pass. But instead of passing, Couture spun to his left and fired a shot through heavy traffic that bounced off a Panther and past Clemmensen.
The goal was Couture's second in two games since returning to the second line at center, after a stint as a first-line winger, and reuniting with Ryane Clowe and Havlat. White earned an assist, his first point as a Shark.
The Panthers countered when Weiss scored a power-play goal at 7:53. With former Panther Boyle in the box for tripping Mike Santorelli, Florida went to work against a Sharks penalty kill that ranked last in the NHL at home and 28th overall. Versteeg set the scoring play in motion when he controlled the puck behind the Sharks net then sent a pass in front to Fleischmann.
Greiss stopped Fleischmann's shot, but the rebound went to Weiss, whose off-speed shot somehow trickled between Greiss and defenseman Douglas Murray and into the net.
San Jose regained the lead when McGinn scored for the second straight game. Third-line center Michal Handzus, skating left to right behind the Panthers' net, whipped a perfect pass in front to McGinn, charging ahead of Fleischmann. McGinn beat Clemmensen to the stick side from close range.
Clemmensen, in his third season with the Panthers after stints with New Jersey and Toronto, started for just his second time this season in place of Jose Theodore. He missed the start of the season while recovering from knee surgery; then made 25 saves in a 6-0 win at Dallas on Nov. 15, but has been battling a groin injury since then.
"I felt good," Clemmensen said. "It's been a while since I played, and obviously that was just one game this whole year. It was important for me to get into the game.
I knew they were a shooting team, so I expected to get some shots early, and I did – the fortunate part. The unfortunate part for me was the first one went in. I knew we were going to get some goals. I've been around the block too many times to let something like that rattle me. It was just a matter of getting a few saves in and getting going. My teammates answered with a goal right after that and we were going. I was going. It was good."
Versteeg, who leads the team in goals and points, returned to the lineup against San Jose after missing Thursday night's 2-1 loss at Los Angeles. He sat out as a precaution after taking a forearm to the head from Carolina's Derek Joslin that triggered headaches and had him concerned he had suffered a concussion. Versteeg said he passed his concussion tests and got over his headaches. Versteeg also suffered a broken nose and a strained neck on the hit – both were still sore Saturday – but those injuries didn't keep him off the ice.
"It just makes a big difference for us," Dineen said. "He gives us other options, and he's a dynamic guy. "He's been a special player for us this year, and he continues to be."