Kilmarnock grabbed the initiative straight from kick-off and pressurised the Dons into a series of mistakes. They capitalised on their good start with the opening goal in the tenth minute that owed a fair bit to luck.
Garry Hay struck a shot from a short free-kick routine that was swerving well wide until Manuel Pascali stuck out his chest and re-directed the ball across goal where Allan Russell was lurking. There was still a bit for the striker to do, but he drilled a great right-foot shot past the keeper.
Aberdeen had no answer to Craig Bryson's breaking runs from midfield and Zander Diamond was the Dons hero as his outstretched foot deflected a goalbound shot over the bar.
Killie were playing their best football of the season and it was a shock when Aberdeen grabbed an equaliser on the half-hour mark.
Full-back Charlie Mulgrew had wasted a couple of good crossing opportunities, but proved that practice makes perfect as his corner found Miller at the near post and the striker imaginatively flicked his heel and powered the ball in at the near post.
The leveller knocked Killie out of their stride, but they almost went in ahead at half-time, but for a great save from Jamie Langfield to deny Bryson from four yards range.
The entertainment continued into the second half in an end-to-end contest. It was Aberdeen who were providing the moments of class, with one Sone Aluko turn truly outstanding.
If Miller's finish on the half-hour mark was impressive, he outdid himself on the hour with a goal of a man in top form.
There appeared little danger when Darren Mackie sent over a near-post cross, but Miller crouched and deftly floated a header over Damien Rascle and into the far corner of the net.
Aluko should have given Aberdeen clear water when sent clear by Mulgrew, but he delayed his shot, allowing the Killie defence to recover and clear.
Both sides continued to press as time ran out, with Willie Gibson coming closest for Killie with a volley that bounced just over the bar.