Mark Messier scored two goals and Jari Kurri provided four assists to lead Edmonton over visiting Calgary.
The Oilers scored twice in the first period as Paul Coffey got in the first goal of the night at 12:25 and Messier flipped the puck high into the corner of the net at 18:40.
The Flames came back at 4:32 of the second period with a power-play goal from center Kent Nilsson, who sent a low slap shot just inside the corner of the net. Moments later, Wayne Gretzky shot the puck past Pat Riggin on a pass from the corner.
Calgary's Don Lever brought the Flames within one at 8:31 of the middle period.
Calgary tied the score one minute into the third period on a power-play goal by Nilsson in which Oiler goalie Ron Low was injured on the attempted save. He was taken from the game; the extent of his injury was not immediately known.
Glenn Anderson and Messier responded with two goals within 17 seconds to regain the lead. Edmonton's Brett Callighen matched goals with Calgary's Phil Russell before Matti Hagman and Stan Weir scored to put the game out of reach.