A few Blue Jackets fans chanted "We want a re-fund!" in the third period - before their team came back with two third-period goals to almost force overtime.
Havlat has seven goals and three assists in a six-game goal streak.
Peter Bondra and Bryan Smolinski each had a goal and an assist and Patrick Sharp and Martin Lapointe also scored for the Blackhawks, who have won five of their last seven games.
Anson Carter, Ron Hainsey and David Vyborny each had a goal and an assist and Alexander Svitov also scored for Columbus, which dropped behind the Blackhawks into last place in the Central Division. Brian Berard and Rick Nash each had two assists.
Down by 3-0, 4-1 and 5-2, the Blue Jackets drew within a goal on Vyborny's rebound goal with 3:58 remaining. They almost tied it with just under two minutes remaining when goaltender Nikolai Khabibulin stopped Vyborny's shot from the high slot.
The Blackhawks dominated at the outset. Outshooting the Blue Jackets 15-3 in the opening period, they scored three times in a span of 3:38.
At the nine-minute mark, Cam Barker's slap shot from the left point glanced off Radim Vrbata in the slot and resulted in a big rebound that Sharp netted from the edge of the right circle.
Just over a minute later, Havlat passed to the back boards to Tuomo Ruutu, who saucered a centring pass that Smolinski converted for his 12th goal.
The Blackhawks made it 3-0 on their next shot. Havlat ended up with the puck at centre after a giveaway by Berard. Havlat skated past defenceman Rostislav Klesla, who hooked his right arm as he went past, and swooped in alone on goaltender Fredrik Norrena, whose new two-year contract was announced just before the game. Havlat skated to an abrupt stop at the left goal mouth and then reached back to flick the puck past the goalie.
Havlat has three goals and seven assists in five games this year against Columbus.
Norrena was replaced by Pascal Leclaire, who had missed the last 21 games because of knee surgery.
Chicago, last in the NHL on the power play, was 1-for-1 in the opening period after Smolinski's goal with a man advantage. The Blackhawks have outscored Columbus 12-4 in the first period in six games this year.
The Blue Jackets cut the gap to 4-2 with a pair of power-play goals.
Carter's centring pass for Nash went off his stick and to Hainsey for a one-timer with Columbus on a two-man advantage.
After Lapointe's wrister on a rush made it 4-1, Carter scored on a jam shot off Vyborny's nifty pass through the crease.
In the final period, Bondra scored off a rebound of Havlat's shot from the high slot, with Svitov answering with a wrist shot from the right dot and Vyborny closing the scoring by going high over Khabibulin's shoulder to set up the wild finish.
Notes: Chicago evened the series with Columbus at 3-3 this season and coach Denis Savard evened his record with the Blackhawks at 15-15-5 since taking over Nov. 29 . . . Leclaire was making his first appearance since Dec. 22 against Vancouver.