Voynov's blast from the point midway through the second period broke a 2-2 tie and Richard's first tally of the year on a tap-in of a Justin Williams shot with 6:16 left in the game secured the victory for the Kings.
Anze Kopitar and Jeff Carter also scored while Williams provided three assists as Los Angeles broke a two-game losing streak.
Jonathan Quick earned the win, turning aside 18-of-20 shots.
Derek MacKenzie and Derick Brassard found the net for the Blue Jackets, who fell to 3-6-1 on the season.
Steve Mason made 27 saves in the loss.