The Saints pulled away to win 19.9 (123) to 12.4 (76).
St Kilda shot to a 24-point lead in the first term, and led by three goals at the first change, but the Crows fought back admirably to square the ledger by half time, and then managed the first goal of the second half to grab the lead for the first time.
The third term saw the teams going goal for goal, with the Saints sneaking ahead by nine points at the final break. But St Kilda put on a withering final-term burst to power to a hefty win.
Nathan Bock was influential from centre half-back for Adelaide with 25 touches and it was no coincidence that his team struggled when he limped to the bench with an ankle injury early in the last quarter.
Richard Douglas was his side's leading possession winner with 31 while Kurt Tippett and Patrick Dangerfield each kicked three goals.
Montagna was the catalyst for a first-quarter St Kilda blitz with his three goals putting the visitors on the back foot at 24 points down with just 15 minutes played.
The Saints were moving the ball with far greater ease than Adelaide but they failed to hit the scoreboard with that dominance and a late Tippett goal made it an 18-point game at the first break.
Dal Santo helped himself to a couple of goals early in the second as St Kilda looked in ominous form, but the Crows were slowly beginning to get their house in order down back with the run and carry out of defence that was a trademark last year more prevalent as the quarter wore on.
After trailing by 24 points early in the term, Adelaide finished the quarter with a three-goal flurry that sent the teams into half time all square.
Tippett gave the Crows their first lead of the night with the first goal of an absorbing third term that saw the lead change hands six times.
Dangerfield's running goal from 50 was a highlight for Adelaide, but Stephen Milne and Adam Schneider were at their opportunistic best at the other end with two goals apiece putting their side up by nine points at three-quarter time.
But the Crows were as disappointing as the Saints were brilliant in the final stanza - offering little resistance as their opponents seized control of the stoppages and rammed home their dominance on the scoreboard.
St Kilda 5.1 7.2 12.7 19.9 (123)
Adelaide 2.1 7.2 11.4 12.4 (76)
GOALS
St Kilda: Montagna 5, Milne 3, Schneider 2, Dal Santo 2, McQualter 2, Stanley, Ray, Goddard, Gwilt, Gardiner
Adelaide: Tippett 3, Dangerfield 3, Van Berlo, Walker, Petrenko, Porplyzia, Maric, Douglas
BEST
St Kilda: Montagna, Dal Santo, Fisher, Milne, Gilbert, Baker
Adelaide: Douglas, Bock, Tippett, Mackay, Goodwin, Dangerfield
INJURIES
St Kilda: None
Adelaide: Bock (groin)
Reports: Nil
Umpires: Donlon, McBurney, Sully
Official crowd: 28, 708 at Etihad Stadium
The views expressed in this article are those of the author and not necessarily those of the AFL or its clubs