Paul Sheerin's side started brightly and keeper McKay had to be sharp to keep out shots from Scott Wright, Connor McLennan and Frank Ross in the opening ten minutes. Kalvin Orsi also came close but screwed a shot wide when he'll feel he should have hit the target.
Out of the blue, Killie broke the deadlock when former Hearts striker Dale Carrick moved on to a Taylor through ball to beat Adam Collin from twelve yards.
The lead only lasted five minutes though as Scott McKenna found space in the box to powerfully head Dylan Thomas's perfectly flighted corner past McKay.
Both sides were showing plenty of ambition as play raged from end to end and Adam Collin had to be alert to deal with Johnston's fine effort. The Dons were forced to make a change just after the half hour mark when David Dagana replaced a limping Frank Ross.
On the thirty six minute Aberdeen deservedly took the lead. The impressive Connor McLennan was played in by Orsi and shimmied past a couple of Kilmarnock defenders before calmly firing past McKay from ten yards.
The second half continued at a high tempo and Scott McKenna should have increased the lead for Aberdeen but he directed his header past the post. Dylan Thomas and Connor McLennan both came close with headers as the Kilmarnock defence struggled to keep their opponents at bay.
Fourteen year old Terry Taylor was introduced to the action with quarter of an hour to play and he made a good impression which augurs well for the future.
However with twelve minutes remaining the visitors hit the Dons on the break as substitute Morrison ran from the halfway line, outpacing his marker, and finishing well from around ten yards.
Unfortunately for Paul Sheerin, his side's habit of conceding late goals came back to haunt them again as Scott McLean picked up Whittaker's pass to beat Adam Collin and claim victory for his team.
A vastly improved performance from Aberdeen who looked good going forward but once again were undone by defensive frailties.