Petrov was born in the village of Prechistoye (Yaroslavl Oblast) and lives in Yaroslavl.
He studied art at VGIK (state institute of cinema and TV).
He was a disciple of Yuriy Norshteyn at the Advanced School for screenwriters and directors (Moscow).
Petrov's style from the late 1980s onward can be characterized as a type of Romantic realism. People, animals and landscapes are painted and animated in a very realistic fashion, but there are many sections in his films where Petrov attempts to depict a character's inner thoughts and dreams. In The Old Man and the Sea, for example, the fisherman dreams that he and the marlin are brothers swimming through the sea and the sky. In My Love, the main character's illness is represented by showing him being buried beneath freshly-fallen snow on a dark night.