Chicago has played 21 games this year and has yet to lose in regulation (18-0-3). That is the longest such streak to start a season in the history of the NHL.
Dating back to last year, the Blackhawks have earned a point in 27 straight games, the third-longest stretch ever. The all-time mark is 35 games, owned by the Philadelphia Flyers.
Chicago twice came from behind to keep the streak alive.
Viktor Stalberg lifted Chicago into a 1-1 tie late in the first period and Patrick Sharp again deadlocked the game with 2:40 left in the second period.
Bryan Bickell gave the Blackhawks a 3-2 lead late in the middle stanza, but Columbus forced overtime when Ryan Johansen scored on a backhander with 7:37 left in regulation.
Seabrook's winning goal came 3:23 into overtime and made a winner out of Ray Emery, who stopped 19 shots. Steve Mason surrendered all four Chicago goals on 35 shots. The Blue Jackets have lost four in a row.