The 19-year old forward, who came on as a second-half substitute for fellow debutant Vitinho, netted with his first touch in senior football after joining CSKA in January 2012 and working his way into the squad from the second team.
CSKA have 20 points from eight matches, six more than the chasing pack headed by city rivals Spartak, who were away to 11th-placed Volga Nizhny Novgorod in the other lunchtime kickoff, and Zenit St. Petersburg who host struggling Terek Grozny later on Saturday.
Rostov goalkeeper Stipe Pletikosa kept CSKA at bay in the first half, denying Nigeria striker Ahmed Musa from close range before he clawed out a curling shot by Brazilian Vitinho, who signed a five-year deal with CSKA this month.
The Croatian palmed away Musa's header from two metres shortly after halftime but was powerless in the 70th minute when Bazelyuk got on the end of a crisp Musa cross from the left after the livewire forward was put through by Swiss midfielder Steven Zuber.
Pletikosa denied CSKA a second goal in the closing stages when he parried a ferocious shot by Japan midfielder Keisuke Honda from 20 metres.(Zoran.Milosavljevic@thomsonreuters.com)