The likes of Elena Baltacha, Heather Watson and James Ward all failed to get beyond the first hurdle, but Robson has ensured that the British participation will stretch beyond Andy Murray for at least another round.
Nineteen-year-old Robson moved around the court the better of the two players during the first few exchanges, but she was unable to make an early breakthrough.
However, in the eighth game and facing two break points, Kirilenko sent down a weak serve and Robson responded by producing a forehand winner for a 5-3 lead. She then held her next service game to claim the first set.
That put the Brit in the ascendancy and she went on to break on two separate occasions for a 4-1 advantage in the second set.
She then surrendered one of those breaks back to her Russian opponent, but the left-hander regained her composure to hold her next two service games and in doing so secured her slot in round two, where she will face Mariana Duque-Marino.