Los Angeles reached 55 points for the season, leaving the Kings tied with San Jose for the No. 4 seed in the Western Conference. Vancouver also has 55 points, but the Canucks lead their division and a division title will ensure them one of the top three seeds.
The loss left Columbus in a precarious position in the playoff race, although the Blue Jackets finished the night in the eighth and final post-season position.
Columbus has only a two-point lead over both Dallas and Detroit and both those teams have two more games to play than do the Blue Jackets.
One of the three games left on the Columbus schedule will be at Dallas next Thursday.
Los Angeles took the lead in the first period on a power-play goal from Drew Doughty, but Columbus tied it 12:07 into the second on Dalton Prout's slap shot.
Clifford also scored on a slap shot less than 2 minutes later for the game-winner.