Clifford collected a long pass from Rob Scudari as he was coming out of the penalty box on the play, skated in alone on Dwayne Roloson and beat the Lightning goalie for the decisive tally midway through the period.
Dustin Penner and Anze Kopitar also found the net, and Jonathan Quick made 24 saves as the Kings broke a two-game losing skid.
Roloson stopped 17-of-20 shots but it wasn't enough to prevent a second consecutive loss for Tampa Bay.
Steven Stamkos collected his NHL-best 35th goal for the Lightning.
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