The Swans withstood a strong first-half challenge before pulling away for a 15.14 (104) to 11.12 (78) victory at Mount Barker on Saturday.
West Coast outscored an opponent in a quarter for the first time this season - kicking 5.6 to 3.2 in the second term - and held a narrow five-point lead at the main break.
But they were overrun in the second half as Sydney's class prevailed in front of 9225 fans.
Making matters worse for the Eagles, Luke Edwards was substituted out with a hamstring injury and Ryan Maric was taken to hospital with rib damage after he was cannoned into by teammate Jack Darling in a marking contest.
Heeney (26 disposals, seven clearances) and Gulden (27, seven) stepped up at the right times and kicked two goals each - a tally matched by Will Hayward, Joel Amartey and Logan McDonald.
James Rowbottom (19 disposals, six clearances) and Nick Blakey (25 touches) were also busy and Brodie Grundy was influential in the ruck as the Swans enjoyed a 44-32 advantage in clearances.
Defender Nick Blakey launches the Swans into attack against the winless Eagles. (Michael Errey/AAP PHOTOS)
Grundy had a game-high eight of those himself along with 20 disposals and 31 hit-outs.
Much-hyped No.1 draft pick Harley Reid was among West Coast's best and stood out with his strength and aggression around the contest.
He kicked his first AFL goal and finished with 18 disposals in another encouraging performance.
Eagles veteran Elliot Yeo (28 disposals, six clearances) and co-captain Liam Duggan (30 touches) battled hard while defender Jeremy McGovern fought on despite losing teeth in a collision with Braeden Campbell.
Duggan won the toss and chose to kick against a handy breeze that Sydney couldn't take full advantage of in the opening term.
The Swans had the first eight inside-50s but found themselves behind when Reid snapped truly and Cripps slotted a superb set shot from the boundary.
The Eagles' pressure was up throughout the first half and Reid's bullocking work was a highlight, as was Jack Petruccelle's huge mark on the back of teammate Maric.
Sydney added four goals to one with the breeze in the third quarter and a crucial 50m penalty against Reid - for encroaching in the protected area - allowed Hayward to give the Swans a 15-point buffer at the final change.
Local product Matt Roberts pounced to kick the opening goal of the last quarter and Sydney kept their opponents at arm's length from there.
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