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Anze Kopitar also scored for the Kings, who are 15-0-1 when scoring three goals or more. Jonathan Quick, who entered with a 2-0-0 record and 0.38 goals-against average in three games against Tampa Bay, made 24 saves.
"Usually when we do get three we're pretty safe with (Quick) back there, obviously," Kopitar said. "He kept us in the game in the first period. That's all you want from your goaltender."
After withstanding pressure in the defensive end, the Kings took a 2-1 lead when Clifford scored on a breakaway off a long pass by Rob Scuderi at 10:16. The goal came 8 seconds after Clifford finished serving a roughing minor.
"We have to be aware of the guy coming out of the box," Lightning coach Guy Boucher said. "We didn't make many mistakes, but it almost seemed that every single one that we made cost us."
Penner made it 3-1 from the slot with 2:14 left in the period.
Steven Stamkos got his NHL-leading 35th goal on his 22nd birthday for the Lightning, who are 6-1-1 in their last eight games.
Stamkos tied it at 1 from the low slot off a pass from Teddy Purcell during a 2-on-1 at 7:49 of the second. The center now has scored at least one goal against all 29 opposing teams he has faced.
Kopitar put the Kings up 1-0 when he beat Dwayne Roloson on an in-close deflection 2:47 into the game. Los Angeles has just 24 first-period goals this season and has led entering the second 12 times.
"Their goaltender stands on his head," Boucher said. "That's the story of their team. I know they're looking for more scoring, but the reality is they've been winning their games 1-0, 2-1, 3-2, and they're having a party."
The Kings were coming off road losses at St. Louis and Carolina in which they were outscored 3-1.
"Guys are really bearing down, and as a team we want to score more goals," Clifford said. "Our goaltenders and our defensive game have really kept us in most games, and we just want to try to improve on our offensive game. So we're just trying to bury as many chances as we can."
Stamkos had a pair of good scoring opportunities stopped by Quick during the first. Martin St. Louis, who had his nine-game point streak end (six goals, 16 points), just missed scoring on a late-second backhander.
"I thought we had some chances," Stamkos said. "We knew it was going to be a tight-checking game, and that's what it was."
Roloson, who lost his starting role this season after leading the Lightning to the Eastern Conference finals last year, has played in just two of Tampa Bay's last eight games. He stopped 17 shots.
Los Angeles center Mike Richards stopped a personal eight-game point drought by assisting on Penner's goal.
It was the Kings' first game at Tampa Bay since a 2-1 shootout victory on Nov. 14, 2009.
Stamkos got a shaving cream pie in the face from his teammates during the morning skate. ... Tampa Bay D Marc-Andre Bergeron (back) and RW Adam Hall (left biceps) were back after missing nine games and 12 games, respectively. ... Los Angeles D Matt Greene assisted on Kopitar's goal for his first assist in 29 games. ... Tampa Bay D Evan Oberg, recalled from Norfolk of the AHL for the eighth time since being obtained in a Dec. 2 trade with Florida, was a healthy scratch. He has appeared in just one game with the Lightning. ... Richards has scored one goal in his last 19 games.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Kyle Rehman, Eric Furlatt Linesmen: Jonny Murray, Pierre Racicot
Attendance: 16,489 (85.9% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Anze Kopitar (17)
Assists: Matt Greene, Justin Williams
Steven Stamkos (35)
Assists: Teddy Purcell, Eric Brewer
Kyle Clifford (4)
Assist: Rob Scuderi
Dustin Penner (5)
Assists: Mike Richards, Jarret Stoll