The Swans kicked the first 11 goals of Saturday night's match on the way to the stunning 24.19 (163) to 4.11 (35) victory in front of 50,723 fans at Optus Stadium.
Heeney, on his return from a hamstring injury, was the star of the show with 26 disposals, 12 score involvements, 518m gained and four goals to go with a stunning mark-of-the-year contender over the top of Harley Reid.
Curnow, who had kicked just five goals in his first three games for the Swans, kicked 4.2, while Brodie Grundy (28 disposals, 33 hitouts, nine clearances, one goal) was a monster in the ruck.
It was a memorable way to celebrate the 200-game milestone of Swans forward Tom Papley, who finished with two goals and three goal assists from 24 possessions.
The result boosted Sydney's record to 3-1 ahead of their Gather Round clash with Gold Coast.
West Coast, who were riding high following comeback wins over North Melbourne and Port Adelaide, slipped to 2-2 and will now have to digest the fifth largest loss in the club's history.
"We're not anywhere near where we need and want to be," Eagles coach Andrew McQualter said when comparing his team to the competition's elite sides.
"Clearly, playing the best teams in the comp, we can't get any part of the game really on our own terms."The Swans to me, to my eye and every bit of data today, they were as good a team as I've seen this year. Clearly their back-half ball movement is electric."We had plenty of plans in place, but we were not able to stop them. I thought their speed, their zip, their reaction, was at a completely different level to ours."
Star Eagles playmaker Harley Reid, without the help of fellow midfield bulls Elliot Yeo (groin) and Deven Robertson (suspended), was restricted to just 17 disposals and one clearance under the tight attention of tagger James Jordon.
Sydney's Angus Sheldrick could be in strife after unleashing a forearm to the head of Reuben Ginbey in the final quarter.
Malcolm Rosas was a late withdrawal for the Swans with a calf injury.
Heeney tore the game open from the outset, tallying 10 disposals, four clearances and a major as Sydney slammed through six goals to nil in the opening term.
"He's been doing it for years," Sydney coach Dean Cox said of Heeney.
"His work as an on-baller, his ability to push forward - he stands up in big moments.
"A lot of people probably see goals and speccy marks, but he's selfless, team orientated, and he's our vice captain for a reason."
The onslaught continued in the second term, with Papley's snap on the run and Chad Warner's double fend-off among the many Swans highlights.
Remarkably, when Sydney had 11 goals to their name compared with West Coast's zero, the inside-50m count was level at 25.
The Eagles' first goal of the match came at the 25-minute mark of the second quarter when Jake Waterman snapped truly on the run, but it was already game over by that point.
The margin hit 100 points when Heeney kicked his fourth goal at the 20-minute mark of the third term, and Sydney never let up.
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