Los Angeles made it 1-0 eight minutes into the first period.
After that, the teams took turns to score the goals until the 2-2 situation before the third period.
With just over ten minutes left in the third period, the decision came.
Kempe, who is in his seventh season in Los Angeles, was assisted by Kevin Fiala who pushed the puck forward to the Swede who was able to direct it into the goal.
26-year-old Kempe's 15th goal of the season.
The match ended 3-2 and the Kings took their seventh win in the last nine games.