The Georgian champions will take a telling lead to Moldova thanks to two first-half goals from Jaba Dvali and one from Nikoloz Gelashvili.
Georgian champions FC Zestafoni defeated FC Dacia Chisinau 3-0 in the opening instalment of their second qualifying round tie.
Both clubs were making their debut in the UEFA Champions League but it was Zestafoni who appeared most at home throughout. Their Moldovan counterparts face a sizeable task on home soil next week after falling to two first-half goals from Jaba Dvali and one from Nikoloz Gelashvili.
Though it was Gelashvili who had the honour of scoring Zestafoni's first-ever goal at this level on 14 minutes, it was captain Tornike Aptsiauri's splendid pass which ensured the No9 of a comfortable finish.
Dvali was equally composed midway through the opening period when he pounced on a lax Dacia offside trap and kept his cool with only visiting goalkeeper Artiom Gaiduchevici to beat.
He doubled his own tally five minutes from half-time to put Zestafoni three to the good, and though Igor Dobrovolski's charges limited the damage after the interval, they will nevertheless have their work cut out in the return on 20 July.
By Vakhtang Bzikadze from David Abashidze Stadium, www.uefa.com