Shamrock Rovers are still seeking their first point in the Europa League after defeat by Rubin Kazan in Russia.
Nelson Haedo Valdez slotted in for the hosts before Ken Oman equalised with a header from Ronan Finn's free-kick after 12 minutes.Rubin moved 2-1 ahead before half-time through Bebars Natcho's low shot.
Valdez fired past keeper Ryan Thompson for the third and Obafemi Martins netted from close range before Karl Sheppard hit the bar for Rovers.