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. Penner made it 3-1 from the slot with 2:14 left in the period.
Anze Kopitar also scored for the Kings, who are 15-0-1 this season 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.
Steven Stamkos got his NHL-leading 35th goal on his 22nd birthday for the Lightning, who are 6-1-1 over 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.
The Kings were coming off road losses at St. Louis and Carolina in which they were outscored 3-1.
Stamkos had a pair of good scoring chances 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.
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.
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.
Notes: 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.