The Dons lead 3-0 after a tremendous result from the first leg encounter in Croatia last night.
Unless they suffer a dramatic collapse it is likely they will face Kairat, who also enjoyed a 3-0 first leg victory against Alashkert, albeit on home turf.
Kairat reached the second round after handily disposing of Red Star Belgrade, before meting out a similar punishment to Alashkert, the side who knocked out St Johnstone over two legs in the previous round.
Former Kairat stars include ex-Aberdeen midfielder Stuart Duff and Kilmarnock hero Alexei Eremenko.
The third round tie will be played over two legs on 30 July and 6 August.