The Eagles conceded the initial four goals but still triumphed, winning 20.16 (136) to 16.9 (105) at Adelaide Oval.
Five talking points: Adelaide v West Coast
Adelaide could slip out of the top eight by the end of the round, despite the efforts of their key forward Taylor Walker, who kicked four goals.
The Eagles, in 11th spot, remain a mathematical chance of sneaking into the finals after a heroic win inspired by Kennedy, Andrew Gaff (three goals, 31 disposals), Matt Priddis (31 touches) and Luke Shuey (30 possessions), while Jack Darling kicked three goals.
West Coast's coach Adam Simpson simply saw the victory as "reward for effort".
"I think our intent and endeavour has been there for a while…hopefully it just shows things we are doing are working," Simpson said.
"It's pleasing, definitely pleasing, I'm pumped."
The Crows were well-served by midfielders Brad Crouch (30 touches) and Scott Thompson (31 disposals) and Josh Jenkins and Eddie Betts potted three goals each.
But Adelaide folded meekly late: they led by two points at the start of the last term but were over-run.
Coach Brenton Sanderson was understandably angry after the game but he said the reason for the result was relatively simple - his side was outworked.
"They were cleaner, they were sharper around the contest," Sanderson said.
"After the boys dug their heels in to get back in front… to be outscored one goal to six goals, five behinds in the last quarter, that's the part that really makes us angry and really frustrates us.
"In the coach's box, in the change rooms, players are obviously feeling the same – I'm sure our fans are exactly the same… we let a great opportunity slip today."
The Crows had launched an early blitz, kicking four goals in the initial 10 minutes to thrill their parochial 49,470-strong home crowd.
But the unfancied Eagles rallied in style: by the eighth minute of the second stanza, the visitors had turned their deficit into a 24-point lead.
With Gaff and Priddis ruling the midfield, the visitors held a 12-point break at half-time before Adelaide responded with six goals to four in the third term to sneak to a two-point advantage at the final change.
But despite seemingly having more to play for than the Eagles, the Crows were overwhelmed in the last quarter, with West Coast kicking the opening five goals, including three more majors to Kennedy.
The key Eagles forward benefited from his Adelaide opponent Daniel Talia being substituted from the game at half-time. The Crows defender was concussed when copping an accidental knee to the cheekbone from Kennedy.
Watch Josh Kennedy corral Brodie Smith on the goal-line
ADELAIDE 6.0 9.2 15.7 16.9 (105)
WEST COAST 5.5 10.8 14.11 20.16 (136)
GOALS
Adelaide: Walker 4, Jenkins, Betts 3, Crouch 2, Sloane, Dangerfield, Martin, Wright
West Coast: Kennedy 5, Gaff, Darling 3, Cripps, Ellis 2, Mackenzie, Hutchings, Hurn, Lycett, LeCras
BEST
Adelaide: Jacobs, Crouch, Walker, Jaensch, Sloane, Thompson
West Coast: Gaff, Priddis, Hurn, Mackenzie, Kennedy, Shuey,
INJURIES
Adelaide: Talia (concussion), Podsiadly (broken nose)
West Coast: Nil
SUBSTITUTES
Adelaide: Daniel Talia replaced by Mitch Grigg at half time
West Coast: Xavier Ellis replaced by Dominic Sheed at three-quarter time
Reports:
Adelaide: Nil
West Coast: Nil
Umpires: Mitchell, Fleer, McInerney
Official crowd: 49,470 at Adelaide Oval
Eric Mackenzie fought a great battle with Taylor Walker all afternoon. Picture: AFL Media