Sholl collected 17 disposals as the Crows booted four goals to none in the last term to win 10.11 (71) to 5.9 (39) at a rain-soaked Adelaide Oval.
The Saints managed only two goals after quarter time and slip to 15th on the ladder, with Adelaide replacing them in 14th spot.
The Crows' triple club champion Rory Laird (31 disposals, 13 tackles) revelled in the wet, as did Jake Soligo (25 disposals) and captain Jordan Dawson (26 disposals).
Crows veteran Rory Laird (C) had plenty of company as he chased possession at Adelaide Oval. (Matt Turner/AAP PHOTOS)
St Kilda defender Nasiah Wanganeen-Milera collected a team-high 29 possessions and Mattaes Phillipou impressed with 20 possessions and a classy third-term goal.
Mason Wood and Cooper Sharman kicked two majors each while Hunter Clark (21 touches, eight clearances) and the recalled Zak Jones (20) were busy.
The Saints led 3.3 to 2.1 at quarter time, with Sharman slotting two set-shots and Phillipou prominent with eight disposals including three clearances.
But the tide turned in the second quarter as the Crows scored three goals to one to take a four-point halftime advantage, 5.5 to 4.7.
"That is probably, in the end, the most pleasing part - we were able to turn the game around," Crows coach Matthew Nick said.
"It showed some maturity."
Heavy rain continued throughout the third term, resulting in a scoring stalemate as both sides failed to kick a major for almost 23 minutes.
The deadlock was broken in style by the Saints' Phillipou, who bounced through a 55 metre goal when near the boundary line.
50 out on the boundary in the wet...— AFL (@AFL) Mattaes Phillipou, that is sensational!#AFLCrowsSaints pic.twitter.com/Q2bQ9HzPxHJuly 13, 2024
That strike got St Kilda to within one point but the Crows responded two minutes later when Sholl neatly collected a half-volley in the goal square and converted.
Adelaide held an eight-point buffer, 6.10 to 5.8, at three-quarter time and gained precious breathing space 11 minutes into the last term when Billy Dowling goaled.
Comeback Crow Riley Thilthorpe then sealed victory with consecutive goals in his first game of the season since recovering from a knee injury.
"They (Adelaide) handled the conditions better," Saints coach Ross Lyon said.
"They're tackling was a bit stronger, their clearance work ... they have been cleaner."
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