Jarome Iginla moved into a tie for the league lead with his 39th goal.
Coming off a 3-0 blanking of St. Louis, Turek stopped 12 shots in the first period, two in the second and eight in the third for his third shutout of the season and 27th of his career.
Marcus Nilson gave Turek all the support he needed midway through the first, scoring his fifth goal in nine games since being acquired from Florida.
Craig Conroy doubled the lead in the second before Iginla scored 41 seconds into the third to pull even with Columbus' Rick Nash and Atlanta's Ilya Kovalchuk in the race for the Maurice Richard Trophy.
Calgary moved seven points ahead of ninth-place St. Louis in the Western Conference. The Flames have missed the playoffs seven straight years