Both sides smashed each other into exhaustion with punishing defence and a fast-paced game with Australia centre Josh Dugan saving two probable tries with his positional sense and a desperate ankle tap on his opposite number Kallum Watkins.
The only thing that separated the sides was Cordner's 15th-minute try as they both controlled the ball well, but England rued stupid errors or poor decisions early in the tackle count inside the Kangaroos' 20-metre area.
"It's amazing to finally get a World Cup victory on home soil," Kangaroos captain Cameron Smith said. "It was one of the toughest football games I've played in my career. A really pleasing victory for the boys.
"We spoke about defence winning games and winning tournaments and we just kept turning them (England) around."
Smith's team had been virtually unbackable favourites for the final after they romped through the tournament, while England had to overcome the weight of history with a 12-game losing streak to the Kangaroos and not having won the title since 1972 as part of the Britain team.
The intensity of the game was set in the first hitup by England prop James Graham when he smashed into four Australian tacklers and reeled away with a cut above his left eye after an accidental head clash with Matt Gillett.
The Kangaroos, who hammered away for much of the opening quarter at England's line, however opened the scoring in the 15th minute when Cordner crashed over during their third successive set of possession.
A superb chase game by England on Luke Gale's tactical kicks, however, gave Wayne Bennett's side field position only for errors and penalties to allow Australia to escape.
Kangaroos standoff Michael Morgan crossed early in the second half but video referee Ben Thaler called it back for interference earlier in the play.
Jermaine McGillvary and Watkins also stormed into open field, only for desperate Australian defence to again snuff out the opportunities.
"Tough one to take," England's Graham said. "Both teams played well. 6-0 doesn't advertise it as a great game but what a spectacle."