Defenseman Paul Coffey scored two goals, including his seventh of the playoffs, to start a five-goal second-period for host Edmonton, which advanced to the semifinals. Oilers goaltender Andy Moog posted 39 saves on shots by Calgary.
The Oilers, who outscored the Flames, 35-13, in clinching the best-of-seven Smythe Division final series in five games, will open the Campbell Conference finals at home Sunday against the Chicago Black Hawks, also a winner in five games over the Minnesota North Stars.
The 35 goals allowed the Oilers to break by one the record for most goals in a Stanley Cup playoff series held jointly by Montreal (established in six games in 1973) and Philadelphia (set in seven games in 1976).
Coffey, who led NHL defensemen in scoring with 29 goals during the regular campaign, opened the scoring on a power play at 12:09 of the first period and set off a surge of five goals in the second period with his seventh goal in post-season competition at 1:39.
The goal came only one second after Calgary captain Phil Russell had returned to the ice from serving his second penalty of the contest. Coffey took a pass at the blue line from Charlie Huddy and blasted a shot high over Calgary goalie Don Edwards' glove hand.
Defenseman Randy Gregg made it 4-0 with a short-handed goal at 3:42. It was the Oilers' fifth of the series and allowed them to tie the record set by the Rangers in 1979. Edmonton, with eight short-handed goals in postseason play to date, is one away from tying the club mark for an entire playoff set by the Islanders in 1981.