The British number four's serving was patchy on the Italian clay - she fired in six double faults - but she was still far too god for her Ukrainian opponent.
Next up for Robson will be second seed Roberta Vinci who defeated Karin Knapp 6-2 6-2
Home favourite and 2008 champion Sara Errani is the top seed at the event and she safely negotiated her way past Romania's Edina Gallovits-Hall 6-1 6-1 in the opening round.
Third seed Julia Goerges of Germany also progressed with a 6-4 7-6(8) victory over Uzbek Akgul Amanmuradova.
Fourth seed and defending champion Anabel Medina Garrigues is out though. She was hoping to win the event for the fifth time but lost 6-1 6-3 to Italy's Maria Elena Camerin in the first round.