After a disappointing first half, Smith, who has only just returned from injury, struck twice in the space of ten minutes at the start of the second half to provide the spark for an emphatic 4-0 win.
Aberdeen had a decent start to the game, but for every chance they created, Copenhagen had an even better one at the other end.
The Reds' best chance of the first half came after just five minutes as Lee Miller beat of the offside trap before pulling his effort wide from the edge of the area.
Canadian international Atiba Hutchinson troubled the Aberdeen defence early on, testing the nerves of Jamie Langfield in the Dons goal with a rising shot that went just over the crossbar. William Kvist also had an effort that went wide of the target.
It wasn't long before the visitors did start to find the target, although Langfield proved tough enough to survive the early test. He gathered Jesper Gronkjaer's shot with little difficulty, while Hutchinson's headed effort had accuracy but not enough power to beat the keeper.
Aberdeen needed to come out fighting at the start of the second half and they couldn't have hoped for a better start than they got when Smith blasted in his spectacular effort less than two minutes after the restart.
He timed his run perfectly to pick up a long ball out of defence before lifted his right-footed effort straight over the keeper from 30 yards out.
As the Dons' confidence soared the Copenhagen defence crumbled and it wasn't long before Aberdeen looked like scoring another. Zander Diamond's effort took a deflection into the sidenetting before Smith struck again.
In a mirror image of his first shot, he latched on to a Miller ball from the halfway line before firing in with his left foot into the corner of the net from over 20 yards out.
It could have been a memorable hat-trick for Smith but his third effort went just wide of the upright.
But that wasn't the end of the night for Aberdeen who continued to push the demoralised visiting defence.
Mikael Antonsson turned the ball into his own net under pressure on 71 minutes, before substitute Rickie Foster knocked in a fourth in the closing minutes.