Vyborny's 15th goal tied it 2-2 at 5:02 of the third period. In overtime, the Blue Jackets were on the power play when Ron Hainsey skated to the top of the left circle and passed across the ice to Vyborny on the right wing. Vyborny's quick shot beat goalie Mathieu Garon inside the near post.
The victory was the Blue Jackets' third in a row. The Kings dropped their third straight.
Geoff Platt scored his first NHL goal and added an assist, giving him four points in two games. Vyborny assisted on Platt's goal.
Kevin Dallman scored his first goal in almost a year for the Kings, and Jamie Heward added a power-play goal.
Fredrik Norrena had 27 saves to run his season record to 18-15-3 in his quest to become the first Columbus goaltender to finish a season with a winning record.
Platt, coming off a strong game Saturday in Phoenix in which he had four shots and two assists, didn't have a good view of his goal.
Rick Nash came down the right wing and traded passes with Vyborny in the middle. Nash sent a centring pass to Platt, who was upended and flew through the air as he tipped the pass into the net.
The Kings came back with two goals in the second period.
Dallman scored his first goal in 51 games when his wrist shot from the left wing slipped by Norrena. Dallman hadn't scored since April 8, 2006.
Just 10 seconds after Platt went to the penalty box for hooking, the Kings took the lead. Michael Cammaleri skated toward the net along the goal-line and slipped a pass under the stick of Hainsey for a one-timer by Heward for his fifth of the season.
Heward spent two years with the Blue Jackets, playing 97 games from 2000-02, posting 12 goals and 18 assists.
Notes: Nash set a career high with his 24th assist. ... Before the game, Columbus general manager Doug MacLean said G Pascal Leclaire (knee), D Duvie Westcott (concussion), D Bryan Berard (back) and F Dan Fritsche (lacerated wrist) won't play the rest of the season. ... Los Angeles C Anze Kopitar missed his third game because of a strained muscle in his upper body.