Babchuk scored 2:52 into overtime and the Hurricanes beat the Phoenix Coyotes 4-3 after squandering a three-goal lead Saturday night. Carolina went 4-3 on the seven-game trip.
"This was the last game for us at the end of 20 days," Babchuk said. "We really wanted to win that for sure. I'm glad we won."
Carolina opened the season with two games in the Czech Republic against Minnesota before returning to North America for five road games, stretching from Ottawa to the West Coast to Phoenix.
The Coyotes trailed 3-0 at the start of the third period, but Kyle Turris led the comeback with a pair of goals and an assist. He scored his first goal in 18 months with 14:15 left in regulation, beating goalie Cam Ward with a wrist shot from inside the right circle.
Turris pulled Phoenix to within 3-2 from a tight angle to the right of the crease with 2:02 remaining. Just 22 seconds later, Turris badgered Ward into a turnover behind the net and sent the puck out front, where Scottie Upshall fired a shot into the semi-open net to make it 3-3.
"I was just trying to hit his stick, give him a hard time and get the puck," Turris said. "Luckily enough he missed it."
Babchuk scored from the side of the left post off a pass from Joni Pitkanen for the game-winner.
"We gave up three, but instead of falling into the dirt and you and me talking about what happened, we won a game on the road," Hurricanes coach Paul Maurice said. "After about the 10-minute mark we were a good team for the next 45 minutes."
Wojtek Wolski added a pair of assists for the Coyotes, who have lost four of five -- including two overtime defeats.
"Full marks for finding a way to get a point," Phoenix coach Dave Tippett said. "But if that's the way we're going to play we're not going to be successful too often."
Dwyer gave the Hurricanes a 1-0 lead 4:17 into the second period. He blocked a shot at the top of the Carolina zone and skated the length of the ice before shooting between Ilya Bryzgalov's pads for a breakaway short-handed goal.
Jokinen made it 2-0 at 9:45 of the period with a power-play goal off a backhanded rebound of a loose puck at the top of the crease.
Samsonov capped the scoring for Carolina after Phoenix defenseman Keith Yandle fumbled the puck behind his net. Brandon Sutter fed the puck to Samsonov between the circles for a one-timer 1:20 into the third period.
"They're a transition team," Tippett said. "They feed on that."
Turris matched a career high with two goals. His last goal was scored March 17, 2009, against San Jose. ... Two nights after the Coyotes drew a crowd of 6,706, Saturday's attendance was announced as 8,189. The Coyotes were without captain Shane Doan, who served the second game of an NHL three-game suspension for checking Anaheim's Dan Sexton in the head. This was the lone meeting between these teams this season. Samsonov, a healthy scratch Wednesday in Los Angeles, has two goals in his three games.