Ebony Marinoff and Anne Hatchard were outstanding, while Courtney Gum showed her class in the second half to help turn the game.
The loss was tough on the Saints, who for much of their second game had looked on target to claim a historic and remarkable first win.
Georgia Patrikios showed a bright future with 18 effective touches, while Tilly Lucas-Rodd, Tarni White and Nat Exon all had their moments.
The Saints weren’t helped when Clara Fitzpatrick was forced from the ground on a stretcher in the last quarter with concussion after a courageous marking attempt.
Adelaide’s 2019 premiership flag was unfurled before the game but, in the first quarter, it looked like it was the Crows’ game which was unfurling.
Without their superstar co-captains Erin Phillips and Chelsea Randall, they started slowly.
Phillips is on the comeback from the torn anterior cruciate ligament, while Randall is out for the season after tearing her ACL in pre-season training.
The Crows, who failed to score in the first quarter of their opening-round loss to Brisbane, also didn’t get on the scoreboard in the opening term against St Kilda.
Nicole Campbell’s short pass was stolen by Kate McCarthy, the only Saint among five Crows players, and she burst away to score the first goal in the 14th minute.