Anze Kopitar had two assists, and David Rittich made 19 saves for the Kings (11-7-3), who had lost three of four.
Brandon Montour scored, and Joey Daccord made 19 saves for the Kraken (10-10-1), who lost their fifth straight road game.
Kempe scored his 10th goal of the season and fifth in four games to put the Kings up 1-0 at 4:19 of the second period. He beat Daccord with a wrist shot from the high slot to the blocker side.
Byfield, playing his 200th NHL game, made it 2-0 on the power play at 6:03. He scored on a one-timer from low in the right face-off circle that was set up by Kevin Fiala.
Montour cut it to 2-1 at 18:26 of the third period on a slap shot from the left point with Daccord pulled for the extra attacker.
