Beaten in their three previous games, the Swans rediscovered their form to lead at every change en route to a 12.15 (87) to 10.13 (73) victory in front of 39,260 fans at the SCG on Sunday.
Swans midfielder Chad Warner won the Brett Kirk medal as best afield for his 24-disposal, seven-clearance effort.
Winning the rematch of last year's qualifying final, Sydney (3-5) have now beaten GWS in their past five meetings.
"The players are aware that it's one game. We've made some inroads, but we've still got a lot of work to do," Cox said.
"You've got to get to the line and test it. We're in such a ruthless competitive environment that you have to get there as often as you possibly can, and we went away from that last week.
"To the players' credit, they responded well, but we have to go again."
But Sydney will face a nervous wait on the availability of Lewis Melican after the defender was cited for collecting GWS tagger Toby Bedford high in the second quarter.
Melican caught Bedford, who had already tapped the ball forward, with his swinging arm.
Bedford did not appear to suffer a concussion but was sent from the field under the blood rule for a cut to his right cheek.
He was later substituted out at half-time due to the swelling around his eye, replaced by Jake Stringer (three goals).
A suspension to Melican would be a massive blow to an injury-ravaged Swans outfit, with captain Callum Mills (foot), Tom Papley (heel) and Errol Gulden (ankle) among 11 players sidelined.
The Giants (4-4) extended their losing streak to three matches.
GWS midfielder Tom Green led the game with 34 disposals and six clearances, while teenager Josaia Delana - who arranged 80 tickets for family and friends to attend his debut - impressed with five tackles.
There were plenty of spotfires early as the Swans kicked five consecutive goals to set up a 21-point lead at quarter-time.
Giants defender Lachie Ash gave away a 50-metre penalty - and a goal - after a poorly-timed attempt to punch the ball out of a marking James Rowbottom.
It took 20 minutes for the Giants to slot their first major, with Darcy Jones hitting the scoreboard before Aaron Cadman added another.
"The first quarter was where the damage was done, and it was around uncontested marks and (Sydney's) ability to then go off the back of that," Giants coach Adam Kingsley said.
"When you allow Sydney to play that brand, they're really difficult to stop.
"We tightened that up after quarter time, but it was a little bit too little, too late."
So dominant were the Swans in the first term that they took 20 inside-50 entries to eight.
GWS cut the deficit to six points in the second quarter, but Sydney held their nerve.
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