For much of the match the home side held the upper hand, but failed to add to a brilliant individual goal from Sone Aluko on 50 minutes. As a result the Dons became more and more nervous as the game entered the final phase before holding on to a deserved victory.
Careless marking by the Dons defence on three minutes allowed a David Lilley knock-on fall into the path of Manuel Pascali, fortunately for the home side the big defender didn't connect with his shot, allowing Jamie Langfield to gather at the second attempt.
A lightening quick break at the other end saw Aluko carry the ball fully 40 yards before smashing a 25-yard effort just over the crossbar.
The visitors threatened again on 14 minutes, a deep cross from James Fowler looked to be falling onto the head of Conor Sammon, only for Zander Diamond to get the merest of touches to clear the danger.
Danger man Aluko again looked threatening when his 25-yard effort brought an excellent stop from Alan Combe. From the resultant corner kick, Aluko was again unlucky to see his rising effort from 16 yards fly narrowly over.
The visitors had a major let-off on 35 minutes, from a Derek Young corner Lee Miller's powerful downward header saw the ball bounce just over the bar.
On 38 minutes Killie defender Jamie Hamill found space on the right, turning inside Charlie Mulgrew before flashing a great effort across the face of goal and just wide of the upright.
Killie ought to have scored immediately upon the re-start, Mehdi Taouil and David Fernandez combined brilliantly before the latter picked out the driving run of Craig Bryson, whose low ball into the danger area was hacked away by Scott Severin with Sammon lurking at the back post.
Aberdeen countered and took the lead on 50 minutes. An angled ball from Miller found Aluko one on one with his marker, the teenager teased Hamill before crashing in an unstoppable 18-yard effort past the rooted Combe just inside the far post.
Aberdeen nearly added a second on 58 minutes. From Young's corner, Miller's powerful header looked goalbound, until Hamill appeared on the line to knock the ball away.
A clever shot free-kick from Severin picked out the run of Young however the midfielder's effort was comfortably held by Combe.
Aberdeen had a huge let-off on 87 minutes, Bryson ferreted his way pass Jared Hodgkiss before pulling a clever ball back into the path of second-half sub Donovan Simmonds. His first-time effort from 20 yards smashed from the underside of the crossbar before being hacked away by Diamond.
With Killie threatening for an equaliser Aberdeen caught them on the break. Miller held the ball up long enough for Stuart Duff to race on to his through ball, the midfielder drew the keeper before firing in a fierce effort which Combe somehow got a hand to, to parry it over.