Detroit could clinch its third consecutive Central Division title if Nashville gets no points in its game with Chicago on Tuesday night. Hasek tied Ed Belfour and Tony Esposito for eighth on the career shutout list.
Kyle Calder, Todd Bertuzzi, and Kris Draper scored for Detroit.
Fredrik Norrena made 21 saves for Columbus.
Calder got the game's first goal 16 seconds into the third period.
He stole the puck from Ron Hainsey in the left corner of the Blue Jackets' end, knocking Hainsey to the ice in the process. Calder took the puck to the net and beat Norrena with a backhand shot as he was being tripped down by Sergei Fedorov, who was sliding across the crease.
Bertuzzi put in a rebound off a goal-mouth scramble with 2:24 left, and Draper added an empty-met goal with 46 seconds remaining.