Babayan began his musical studies at age six with Luisa Markaryan. He studied under Lev Naumov and at the Moscow Conservatory under Vera Gornostayeva and Mikhail Pletnev. In 1989 Babayan travelled to the United States. That same year he won first prize in the Robert Casadesus International Piano Competition. After he won first prize in the Palm Beach International Piano Competition and first prize in the Hamamatsu International Piano Competition, he became a Laureate of the Queen Elisabeth Music Competition in 1991. He won first prize in the Scottish International Piano Competition and third prize at the Busoni International Piano Competition. He was a prize winner at the Esther Honens International Piano Competition.
His programming often includes Romantic composers such as Rachmaninoff, and modern works by composers such as Lutosіawski, Ligeti, Vine and Arvo Pдrt. He is also recognized for his prominent interpretations of J. S. Bach.
He frequently appears as a soloist with such orchestras as The National Orchestra of Belgium, The Cleveland Orchestra, The Italian Symphony Orchestra of Brescia & Bergamo, and the Czech State Philharmonic.
Babayan has collaborated with such conductors as Valery Gergiev, Yuri Temirkanov, Neeme Jдrvi, Hans Graf, David Robertson, Kazimierz Kord and Michael Christie. He has recorded with the Connoisseur Society label, Discover Records and Pro Piano Records.
In 1996, Babayan founded the Sergei Babayan International Piano Academy at the Cleveland Institute of Music, where he is also an Artist-in-Residence. His students have included the pianist Grace Fong, now Director of Keyboard Studies at Chapman University Conservatory of Music