The Kings trailed in the third period before Dustin Brown scored at 3:49 to make it 3-2 and Arvidsson's second goal of the game tied it 3-3 at 16:14.
Jonathan Quick made 26 saves for the Kings (30-19-7), who had lost two after winning five in a row.
Elvis Merzlikins made 39 saves for the Blue Jackets (28-25-2), who had won five of seven.
"We get to OT there, think we win, and you don't," Columbus coach Brad Larsen said. "Tough to swallow right now."
The Blue Jackets have had eight goals overturned this season after reviews for offside.
"I'm done talking about the offside," Larsen said. "There is nothing more to dissect. We went offside. They took it back."
The Blue Jackets trailed in the second period before scoring the fastest three goals in their history, 46 seconds apart, for a 3-1 lead.
Arvidsson gave the Kings a 1-0 lead at 14:00 of the second.
Patrik Laine tied it 1-1 at 15:34 from the left circle after the puck came off the end boards. He has scored 24 points (15 goals, nine assists) in the past 15 games.
"[Laine] has been clutch for us, scoring goals," Blue Jackets forward Sean Kuraly said. "The game was lopsided for them for a while until he got open. That that made us think 'We are in this thing.'"