The Crowslooked to have done enough in the final term when Jason Porplyzia's goal putthe home side 13 points up.
But a goalto Bradd Dalziell drew the visitors level before Kennedy finished a West Coastcounter attack with just 53 seconds left on the clock.
The winsees the Eagles' finals hopes kept alive, while it all but ends those of theCrows.
West Coastcoach John Worsfold admitted he questioned whether his side could fight its wayback into the match.
"CertainlyI thought it was going to be hard to get back," he said.
"I wasreally pleased with the way we responded to what we had to do.
"Oncewe got behind, the challenge was to take some risks, but also play smart tocreate some scores. And then to defend that obviously."
Neitherside managed to extend its lead beyond 16 points in the grinding contest – amargin achieved by Adelaide after it booted the first three goals of the game.
ShaunMcKernan was brought in to combat Nic Naitanui's athleticism and put his own onfull show with a strong contested mark 50m out, before wheeling around andconverting.
Minuteslater he was reported for a crude elbow to the head of Brad Sheppard that sawthe Eagle temporarily subbed out of the game in the second term withconcussion. Crowssubstitute Matthew Jaensch was also called on early, after Aidan Rileyappearing to badly injure his right ankle.
A miracleJosh Hill mid-air volley on the quarter-time siren capped an impressivefour-goal fight back from the Eagles.
Consecutivemajors to Tom Lynch and Josh Jenkins wrested the lead back for Adelaide and athird for the quarter to Patrick Dangerfield was enough to hold onto the narrowlead at the main break.
The classthat saw Crow Brad Crouch secured a year before his legal AFL debut had himleading the possession-getters at the main break (finished with 26 touches),while Chris Masten ran rampant for the Eagles (finishing with 39 disposals).
A slipperyball combined with the pressure of the contest ensured an ugly game to watch asboth sides routinely turned the ball over.
WillSchofield was allowed to run unchecked into an open goal to put the Eagles backin front and teammate Patrick McGinnity extended the lead to 11 points afterwinning a free kick for throwing his head into vacant space.
Goals toPorplyzia and Matthew Wright put the Crows back in the lead but still theEagles wouldn't go away.
Theysomehow grabbed back momentum off the home team, before drawing level throughDalziell.
With lessthan a minute left in the game a counter attack saw the Eagles outnumber theirAdelaide opponents in attack, with Kennedy delivering the match-winning blow.
Crows coachBrenton Sanderson was left to rue missed opportunities to "ice" thegame late in the final quarter.
"Wejust needed a point, any score would have done, we could have looked for waysto ice the game and we didn't do it," Sanderson said.
"Wemissed too many shots in front of goal, nine goals, 15 [behinds] – we missedsome absolute sodas tonight.
"In aclose game you've got to go back and nail them."
ADELAIDE 3.2 6.5 7.11 9.15 (69)
WEST COAST 4.3 5.4 8.7 11.9 (75)
GOALS
Adelaide:Lynch 2, Porplyzia2, Mckernan, Sloane, Jenkins, Dangerfield, Wright
WestCoast: Kennedy 4,Hill, LeCras, Cripps, Schofield, McGinnity, Embley, Dalziell
BEST
Adelaide:Crouch,Dangerfield, Lynch, Douglas, Henderson, Rutten, Porplyzia
WestCoast: Kennedy,Masten, Naitanui, Priddis, LeCras, Waters, Embley
INJURIES
Adelaide: Aidan Riley (ankle)
WestCoast: Nil
SUBSTITUTES
Adelaide: Matthew Jeansch replaced AidanRiley (knee) in the first quarter
WestCoast: AndrewEmbley replaced Jacob Brennan in the third quarter.
Reports:Shaun Mckernan forstriking Brad Sheppard in the first quarter.
Umpires: McBurney, Stewart, Armstrong
Officialcrowd: 26,426 atAAMI Stadium
