Jason Demers and Tyler Benson scored, and Dylan Holloway and Philip Broberg each had an assist for the Oilers.
Cole Perfetti scored two power-play goals, Pierre-Luc Dubois and Ville Heinola each had two assists, and Connor Hellebuyck made 25 saves for the Jets.
Benson gave the Oilers a 1-0 lead at 14:54 of the first period, intercepting a clearing attempt by Heinola up the boards and scoring on a snap shot.
Perfetti tied it 1-1 at 16:43, knocking in his second rebound attempt during a 5-on-3 power play. He then put the Jets ahead 2-1 at 8:50 of the third period.
Demers, who is in training camp on a professional tryout contract, tied it 2-2 at 11:12 when he scored off a cross-ice pass from Holloway on a 5-on-3 power play.
Devin Shore scored the lone goal in the shootout for Edmonton.
