There is a Ural Airlines flight from Moscow DME to Rimini which is the closest airport to San Marino, works out at about 130 euros per person.
Still 2 flights to get from astana to moscow DME though, all the direct flights fly in to moscow SVO and travel between DME and SVO is more hassle than its worth from what i've read.
At least its just a taxi when you land in Italy though.