The Cats had two opportunities within the last minute to take the lead through Jimmy Bartel and Harry Taylor, but both missed set shots from inside 20m on acute angles.
The result keeps the Crows within two wins of eighth spot and although their finals hopes are incredibly slim, they remain alive.
Adelaide dominated the early stages and should have led handsomely with 19 first-quarter inside 50s to seven.
But while the Cats booted four straight, the home side could only manage five behinds from six very gettable opportunities.
Joel Selwood began his day in fearsome fashion with nine first-term possessions while Richard Douglas had the ball on a string with 14.
Crows coach Brenton Sanderson has lamented "fundamental skill errors" all season and two glaring examples resulted in the easiest of goals to Josh Caddy to put his side up by seven points.
Motlop and Tom Hawkins extended the lead before Selwood showed his class to nail his second; the Cats were in control.
Geelong's only worry during a five-goal-to-one second term was Bartel's high hit on young Crow Rory Laird.
He faces an anxious wait after bumping front-on into Laird as the Crow was hunched over the ball. The 19-year-old rookie was subbed out via the concussion rule, but he returned during the third quarter.
The Crows looked to rein in the flag fancies after the break via consecutive goals to Matthew Wright and Tom Lynch.
A cool Josh Jenkins goal on his non-preferred foot was bookended by Lynch's second and third majors of the quarter, reducing the margin to 14 points.
Adelaide's effort and desire was obvious at the last change and, crucially, the deficit was being slowly eroded.
The first goal of the last shaped as a vital advantage for either side and it was Bernie Vince who stood up – snapping spectacularly on his left foot to draw the Crows to within eight points.
An amazing one-handed mark and conversion from Andy Otten was supported by another classy snap from Brad Crouch before Wright's fourth gave the Crows the lead with less than five minutes remaining.
Bartel and Taylor then both missed tough chances to win the lead back before the clock ran down, gifting the Crows their best win of the year.
Harry Thring is a reporter for AFL Media. Follow him on Twitter: @AFL_Harry
ADELAIDE 3.5 4.8 9.8 14.10 (94)
GEELONG 4.0 9.2 12.4 14.8 (92)
GOALS
Adelaide: Wright 4, Lynch 3, Vince 2, Otten 2, Jenkins, Crouch, Van Berlo
Geelong: Selwood 3, Caddy 3, Motlop 2, Kelly 2, Hawkins 2, Lonergan, Blicavs
BEST
Adelaide: Henderson, Douglas, Wright, Sloane, Lynch, Vince
Geelong: Selwood, Simpson, Enright, Bartel, Corey, Caddy
INJURIES
Adelaide: Nil
Geelong: Taylor Hunt (foot) replaced in the starting line-up by Jesse Stringer
SUBSTITUTES
Adelaide: Mitchell Grigg replaced Scott Thompson in the third quarter
Geelong: Jordan Murdoch replaced Travis Varcoe in the fourth quarter
Reports: Nil
Umpires: Farmer, Dalgleish, Nicholls
Official crowd: 28,603 at AAMI Stadium
