Bartecko scored the game-winner seven minutes after Lasse Pirjeta tied it for the BLue Jackets. The Slovakian took a pass from Tony Hrkac that split two Columbus defenders, skated in and faked a backhander before putting a wrist shot past goaltender Marc Denis for his sixth goal.
Hnilicka got the start after Pasi Nurminen was in the nets in Friday's 5-1 loss to Los Angeles. He responded with his third win in five games, improving to 3-2-1 in his last six decisions on the road.
Dany Heatley tied Ilya Kovalchuk's Thrashers' record with his 34th goal, opening the scoring on the power play with 1:46 left in the first period.
Rookie Mark Hartigan also scored for Atlanta, which improved to 3
Pirjeta and rookie Rick Nash each collected a goal and an assist and Matt Davidson recorded his first career multi-point game with two assists, but the Blue Jackets were denied a third straight win.