Three years later he moved to Dinamo Tbilisi, where head coach Ivo Šušak had already begun his successful period, and won his first title in 2003.

The next year he took part in UEFA Cup group stage matches with Dinamo and scored a vital goal in a 3rd round qualifying game against Wisła Kraków.

[5] In this transitional season to the Spring-Autumn system, his team prevailed over Dinamo Tbilisi in a tight contest for bronze medals.

[6] But the next season Batumi suffered a dramatic loss in a relegation play-off tie against Sioni Bolnisi, which led to Kvirkvelia's departure for Rustavi.

Kvirkvelia made his debut with the Georgia national team in a 0–0 draw to Switzerland on 2 April 2003 in UEFA Euro 2004 qualifying.