FC Olimpi Rustavi 1-1 FK Aktobe (agg: 1-3)
The Kazakh side were unable to convert a hatful of chances and even trailed for an hour in Georgia before Murat Tleshev finally sealed progress.
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FK Aktobe betrayed a few nerves before securing progress to next week's third qualifying round as Georgian titleholders FC Olimpi Rustavi provided a significant test in searing temperatures.
Visitors Aktobe dominated from the off at the Poladi Stadium but found their 2-0 first-leg advantage halved on the half-hour mark when Giorgi Rekhviashvili rose to head in David Bolkvadze's corner. The Kazakh side cranked up the pressure, the lively Konstantin Golovskoy hitting the crossbar midway through the second period, but it was not until the final minute that Murat Tleshev finally sealed progress.
Vladimir Mukhanov's side's next UEFA Champions League opponents will be Hapoel Tel-Aviv FC. His forwards may have to up their game if they wish to avoid elimination by an Israeli side for a second year in succession having lost 4-3 to Maccabi Haifa FC at the same stage 12 months ago.
Time and again Golovskoy was denied by goalkeeper Grigol Bediashvili, and even when the veteran did find a way past on 63 minutes the woodwork denied him an equaliser. Substitute Tleshev missed the target on the rebound, but made amends late on when he nodded home Emil Kenzhisariev's pinpoint centre.