Khabibulin began his 15th year in the NHL and his second season with Calgary by recording the 42nd shutout of his career.
Edmonton had a 1-0 lead heading into the third period thanks to a power-play goal by Gilbert Brule midway through the first. The 20-year-old Eberle scored shorthanded 84 seconds into the third and Ales Hemsky produced a goal on a slapshot 1:09 later.
Eberle added a power-play goal at 5:04 of the third to complete the scoring. Eberle became one of two players to score two goals during the first day of the NHL season and Khabibulin recorded the league's first shutout.
Miikka Kiprusoff stopped 29 shots for the Flames.