Aged 17, Cleșcenco made his debut for Nistru Chișinău as substitute in the 72nd minute in a 1990 Soviet First League match against Kotayk Abovyan.
He played for half of the season at Spartak Oryol, where he was invited by the Moldovan coach Valentin Goian.
After another strong season in Haifa, he moved to Hapoel Tel Aviv, where he was part of the squad that reached the quarter-finals of the UEFA Cup.
[4] He was nicknamed "Kalashnikov" by the Israeli fans after scoring four goals during 30 minutes in a 5–2 win over Hapoel Petah Tikva.
After 6 matches for the Russian side, he returned to Israel, signing for Bnei Yehuda Tel Aviv, scoring one goal in 14 appearances.
[2] Aged 19, Cleșcenco made his international debut as a substitution in Moldova's first official match, a 2–4 loss against Georgia in 1991.
In a 2006 friendly against Lithuania he scored his 11th and last goal for the national team, remaining Moldova's top goalscorer until 2023.
In the same year, he made his 69th and last appearance for Moldova against Bosnia and Herzegovina in UEFA Euro 2008 qualification, which was another record at the time.
The Moldovans lost at penalties and were relegated to 2022–23 UEFA Nations League D. Moldova placed second in its group, being tied to points with Latvia, but had a lower goal difference, failing to achieve promotion.
In UEFA Euro 2024 qualifying Moldova obtained a historic shock 3–2 comeback win over Poland.