"We had a ton of shootouts at the start of the year," Versteeg said. "You just go down there and do whatever you have in your head. You try not to think too much. If it works, it works. If not ... not."
The Blackhawks appeared to have a victory in regulation.
But with Carolina on a power play and Ward off for an extra attacker, the Hurricanes' Tuomo Ruutu scored with 26.5 seconds left to tie it at 2.
After both teams failed in the third round, Versteeg beat Ward to give the Blackhawks the advantage. Huet then stopped Samsonov as the Blackhawks raced to the ice to celebrate the win, one that ended Carolina's four-game winning streak.
"Pucks were going in all over the place," Chicago coach Joel Quenneville said. "It was pretty exciting out there. The game was tight and that's what we're going to see until the end."
Chicago is fourth place in the Western Conference. With the point for the regulation tie, Carolina tied Pittsburgh for sixth place in the Eastern Conference with 78 points, although Hurricanes have one more loss than the Penguins,
"You have to keep winning. If you lose, you're going to be out of the playoffs pretty soon," said Ruutu, a Chicago first-round pick who dealt away last season. "It's always a little emotional, but not nearly like it was last year right after my trade."
Versteeg also had a tying goal in the second period.
In overtime, Ward stopped a partial break by Kane, and Huet blocked a shot by Eric Staal on a breakaway with 3 seconds to go.
Ward finished with 39 saves, and Huet had 29.
"It goes off to chance in the shootout," Ward said. "And they've got some good players who can shoot the puck."
Troy Brouwer gave the Blackhawks a 2-1 lead in the final period. On a power play, Kane skated from behind the net and slid a nice pass to Brouwer for the score.
Chicago's victory snapped a two-game losing streak and came without right winger Martin Havlat, who missed his first game of the season after sustaining a lower-leg injury Sunday in a loss to Colorado.
The Hurricanes opened the scoring at 5:24 of the first period. Rod Brind'Amour was wide open on the side and took a pass across the crease from Samsonov for an easy score.
Ward turned away seven shots during two Blackhawks' power plays in the opening period and also snuffed Kane on a point-blank attempt.
Versteeg scored on a 2-on-1 breakaway in the second, using a wrist shot from the left circle to beat Ward high on the glove side, and the Blackhawks had a tie.
It was Chicago's first win over Carolina since April 3, 1999. The Hurricanes were 7-0-1 against the Blackhawks in that span and had won four straight in Chicago. Wednesday's meeting was the only regular-season one between the teams this season. ... Havlat could play in Friday's game against Columbus. With 21 goals and 36 assists, he is tied for second on the team with 57 points. ... Quenneville coached his 900th NHL game. ... Hurricanes' D Joni Pitkanen sustained a lower-body injury and did not play in the third period.