After the first three rounds of the shootout ended in a 2-2 stalemate, Versteeg's forehand wrister beat Cam Ward just below the crossbar to give Chicago the lead. Sergei Samsonov represented the last hope for Carolina, but Cristobal Huet made the save to secure the win for Chicago, its first over the Hurricanes since 1999.
"I wasn't trying to think too much," Versteeg said. "You try to do your own thing and use it to your advantage. Shoot the puck and hope it goes in."
Troy Brouwer and Versteeg scored in regulation for Chicago, which had lost two straight and five of seven coming into the game. Huet made 29 saves for his 19th win of the season.
"We needed to come out tonight and bring it to them," Versteeg said. "It was a huge game, and all the teams are trying so hard right now to win. We need our own winning streak."
Rod Brind'Amour scored for the third straight game, while former Blackhawk Tuomo Ruutu also tallied for the Hurricanes, who had won four straight and eight of 10. Ward stopped 39-of-41 shots in the loss.
"The standings are so tight, you just have to keep on winning," Ruutu said. "There are six teams trying to get the playoff spots, and it will be a big battle until the end."
The Hurricanes got on the board first, as Samsonov dished across the crease to a wide-open Brind'Amour, who easily tapped the puck into the net at the 5:24 mark of the opening period.
Versteeg tied the game late in the second, wristing a shot past Ward from the left circle while on the rush with 2:52 left in the period.
A four-minute high-sticking penalty on Ruutu killed a Carolina power play and handed the Blackhawks a two-minute man advantage, and the hosts made it count. Patrick Kane skated around the goal and found Brouwer at the other side of the crease, and he tucked it into the net for a 2-1 lead 4:51 into the third.
Carolina pulled Ward in the final moments in an attempt to equalize the game, also receiving a power play with just over a minute to go. The Hurricanes took advantage of the opportunity, as Ruutu scored through traffic from the slot with 27 seconds on the clock, and the game went to overtime.
"It was a good back-and-forth pass for us, and then a hell of a shot," Ruutu said. "It was really awesome."
Kane had the best chance for either team in the extra period, but his shot from in front hit the crossbar, missing a wide-open net, and a shootout was needed to decide the contest.