Kvartalnov had a career which lasted for 25 years, during which he played in North America for the San Diego Gulls of the IHL, the Boston Bruins of the NHL and its minor league affiliate, the Providence Bruins. Kvartalnov's career in Europe consisted of Adler Mannheim in Germany, Jokerit in Finland, HC Ambri-Piotta in Switzerland, Klagenfurter AC in Austria, and teams like Khimik Voskresensk and Ak Bars Kazan in Russia. Kvartalnov retired from play in 2008.
