Schultz finished with a goal and two assists while Hall, Jones and Nail Yakupov each ended with a goal and an assist as the Oilers notched a fourth straight win.
The victory put them just one behind St. Louis for the eighth and final playoff spot in the Western Conference.
Brian McGrattan scored for Flames, who dropped a team-record 11th straight road game.
Miikka Kiprusoff started in net but was pulled late in the first period after yielding three goals on six shots.
Joey MacDonald posted 13 saves in relief.
Celebrity Families of 2014 [PHOTOS]