Kovalchuk matched his season high of four points Wednesday by assisting on Marian Hossa's power-play goal with 31.5 seconds to play in overtime of a 5-4 win at Carolina. Atlanta had blown a two-goal lead in the third period.
Kovalchuk's performance helped the second-place Thrashers (20-20-1) move within three points of the Hurricanes (20-18-4) in the Southeast.
"We want to keep chasing them and keep winning those games," he said. "They're huge games. They didn't play their best game and we're playing pretty good. We've got more chances to win."
Kovalchuk, who leads the league with 33 goals and is among the highest scorers with 57 points, has four goals and six assists in the last four games.
The left wing's 24 goals in 33 career games versus Carolina are his most against any team. He has found the back of the net in five of the last seven meetings and each goal contributed to a victory. However, the two games he was held without a point - both losses - have come at Philips Arena, including a 5-3 defeat on Nov. 10.
Atlanta, though, has since won the last two meetings, including a 3-0 win on Nov. 16 as Kovalchuk had two points.
The Thrashers have never won three straight games against the Hurricanes in a single season.
To do that, they could use a better third-period performance after squandering a pair of leads Wednesday as Carolina forced overtime with three goals in the third.
The Hurricanes also found some positives from outshooting Atlanta 36-14.
"I thought we competed for the whole 65 minutes," Hurricanes coach Peter Laviolette said. "There's a process in order to win a hockey game and I thought the process was correct tonight, but the results were disappointing - definitely not satisfying."
Laviolette's team hopes to avoid extending its losing streak to a season-high four games. The Hurricanes last dropped four in a row from Jan. 27-Feb. 3 en route to missing the playoffs a year after winning their first Stanley Cup.
Carolina's current slide is part of a 9-14-1 stretch that has seen it allow a league-high average of 3.71 goals per game.
The Hurricanes could use a better performance in goal after Cam Ward managed only nine saves Wednesday.
Ward has struggled in his last nine games, going 2-5-1 with a 3.88 goals-against average. He is 1-3-1 with a 3.38 GAA in his last five games against Atlanta. The lone victory, though, came in the last meeting at Philips Arena when he stopped 32 of 35 shots.
Carolina's other option in net has not been playing any better, with veteran backup John Grahame sporting a 2-5-0 mark and a 4.82 GAA in his last eight games.
Hurricanes center Eric Staal, who had a goal and an assist in the third period Wednesday, has scored six goals in nine games to give him a team-high 21. The center has two goals and six assists in his last eight games at Atlanta.