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.
James Paterson's early cross caused problems for the home defence, but Rubin were soon on the attack.
Valdez fired across the face of goal and Martins was off target with an overhead kick before the breakthrough arrived in the 10th minute.
The striker beat Oman far too easily and finished calmly past the advancing Thompson.
Oman quickly made amends when he equalised two minutes later.
Billy Dennehy shot straight at home keeper Sergei Ryzhikov from a narrow angle, with Sheppard better placed in the centre.
However, Shamrock had a let-off when Thompson flapped at a cross and Dan Murray had to clear Martins' effort off the line.
Rubin regained the lead moments later when Rovers failed to clear and the ball broke to Natcho, who finished low with Thompson unsighted.
More sloppy defending saw the League of Ireland side fall 3-1 behind six minutes after the interval as Valdez sauntered past a misjudged offside trap and shot past Thompson.
Martins got his name on the scoresheet although Gokdeniz Karadeniz appeared to take the ball out of play before crossing to set up the goal.
The Nigeria striker curled another effort just wide before Rubin settled for their three-goal margin.
That allowed Shamrock to go in search of a consolation goal, but Sheppard's volley clipped the top of the bar and the same player then had a penalty appeal turned down, with Bocchetti's foul ruled to be outside the box.
The victory takes Rubin up to 10 points in Group A while Shamrock remain bottom.