The Giants looked set for another hefty loss when the Crows surged to a 27-point lead at quarter-time in slippery conditions, but the visitors fought back gamely during the rest of the match.
GWS outscored the home team by four goals in an impressive second term before the Crows eventually slipped away to win 13.18 (96) to 7.8 (50).
Israel Folau kicked his first AFL goal but a four-goal haul to key Adelaide forward Kurt Tippett ensured the Crows comfortably won.
The fledgling Giants trailed by just 17 points at half-time to give the parochial 28,261-strong Adelaide crowd a fright.
But Tippett's influence loomed large in the rain as the Crows overpowered the visitors in the second half.
Tippett was hounded all week for inaccurate goal kicking, but converted two long range set shots in the initial four minutes of the game.
And the Adelaide spearhead booted another two goals in two minutes of the third quarter to snuff out the GWS challenge.
The Crows streeted to a 27-0 score before Folau set up the Giants' first goal, delivering a 40m pass to Curtly Hampton (three goals) - one of just two times the visitors entered their attacking 50m arc in the opening term.
In contrast, Adelaide went inside 50m some 20 times, with two classy snaps from Jason Porplyzia kicking the Crows to a 5.4 to 1.1 quarter-time lead.
But the Giants dominated the second stanza, outscoring Adelaide four goals to two - including Folau's milestone major.
The rugby league convert goaled from almost 50m after a strong mark on the lead to help get the Giants within 17 points of the Crows at the long break.
But Tippett's rapid-fire brace in the third term set Adelaide on course for its third win from four matches, with onballers Rory Sloane, Patrick Dangerfield and skipper Nathan van Berlo all influential.
The Giants' experienced core of Callan Ward, Luke Power and Tom Scully toiled gamely against the Crows, who lost utility Jared Petrenko in the first 10 seconds when knocked out in a collision with his Crows colleague Porplyzia.
ADELAIDE 5.4 7.8 10.13 13.18 (96)
GREATER WESTERN SYDNEY 1.1 5.3 6.6 7.8 (50)
GOALS
Adelaide: Tippett 4, Porplyzia 2, Mackay, Henderson, Wright, Walker, Sloane, Smith, Thompson
Greater Western Sydney: Hampton 3, Edwards, Folau, Giles, Mohr
BEST
Adelaide: van Berlo, Sloane, Thompson, Tippett, Reilly, Doughty
Greater Western Sydney: Ward, Scully, Power, McDonald, Giles, Miles
INJURIES
Adelaide: Petrenko (concussion), Martin (cut head), Jaensch (cut head)
Greater Western Sydney: Nil
SUBSTITUTES
Adelaide: Ricky Henderson replaced Jared Petrenko in the first quarter
Greater Western Sydney: Jacob Townsend replaced Adam Tomlinson in the third quarter
Reports: Nil
Umpires: Ryan, Hosking, Hay
Official crowd: 28, 261 at AAMI Stadium
The views in this article are those of the author and not necessarily those of the AFL or its clubs
