Born in Lomonosov, Russia, Soviet Union, Mostovoi signed for country giants FC Spartak Moscow from second division club FC Presnya Moscow, quickly making an impression. In January 1992, he joined compatriots Vasili Kulkov and Sergei Yuran at S.L. Benfica; months before arriving, he was controversially awarded Portuguese citizenship through marriage, but never imposed himself in the first team.
Midway through 1993–94 Mostovoi joined Ligue 1 side SM Caen, then left after the sole season to fellow French side RC Strasbourg, rejoining coach Daniel Jeandupeux. With the latter, he first displayed glimpses of an emerging talent.
Mostovoi's big break came when he signed for Celta de Vigo in 1996, for 325 million pesetas (about €1,950,000). He made his debut for the Galicians in a 2–0 home defeat against Real Betis, and his creative play and key goals made him a cult figure at Balaídos as the club rose to near the top of La Liga standings year after year.
Affectionately nicknamed 'The Tsar of Balaídos' by the fans, Mostovoi formed an impressive midfield society with, amongst others, compatriot Valery Karpin, and helped Celta win the 2000 UEFA Intertoto Cup. However, he couldn't help the freefall that hit the team in the 2003–04 season, relegating it to the second division after the player appeared in a career-worst (in his Celta career) 24 matches.
Having not played for over eight months, and at the age of 36, Mostovoi signed a contract with Dmitry Pietrman's Deportivo Alavés in early March 2005, initially until the end of the second level campaign. His first and only game came in a league game against Cádiz CF in which he came on as a substitute, in the 78th minute – he scored the Basques' only goal (and nearly added a second) in an eventual 1–3 defeat.
Having been with the club for only 30 days, Mostovoi told the club directors of his intention to retire claiming he was suffering from back problems.
Mostovoi played for the Soviet national team, the CIS and Russia internationally. In another temper tantrum, he was sent home by team manager Georgi Yartsev during the latter's trip to UEFA Euro 2004, after questioning his methods. He played in the Euro 96 and the 1994 FIFA World Cup and was also picked for the 2002 World Cup, but did not play in the latter tournament due to injury.
Mostovoi's exclusion from Euro 2004's national squad happened after the 0–1 group stage loss to Spain. Supposedly, the player talked with the media after the match and gave an interview saying that Yartsev was not a good coach and did not understand anything. This was later proven false, after Mostovoi gave another interview and explained he merely said that Yartsev overworked the players during practice, so they didn't have the necessary energy to play well in matches. All in all, group morale dropped after the incident, and Russia lost the second game to hosts Portugal.
In 2009, Mostovoi was part of the Russia squad that won the Legends Cup.
Mostovoi graduated from college as an electrician, and later joined a sports academy in Moscow, which provided coaching to young players with a university education.
Married to French Stefani, with whom he later had two children.Spartak Moscow
Soviet Top League: 1987, 1989
Primeira Liga: 1993–94
Taça de Portugal: 1992–93
UEFA Intertoto Cup: 2000
Copa del Rey: Runner-up 2000–01
UEFA European Under-21 Championship: 1990
Legends Cup: 2009