Shamrock Rovers became the first Irish side to reach the group stages of a European competition with a famous 2-1 away win over Partizan Belgrade.
Substitute Stephen O'Donnell scored a penalty in extra-time to take his side through 3-2 on aggregate after last week's draw in Dublin.
Vladimir Volkov put the hosts ahead in the 35th minute but Pat Sullivan scored a stunning 58th-minute equaliser.
Rovers were drawn with Tottenham, Rubin Kazan and PAOK in the group stage.
The 16-time Irish champions are aiming to stage their group games at Tallaght Stadium but, under existing Uefa regulations, the Hoops would have to move their games to Dublin's Aviva Stadium. The alternative would be to install seats at Tallaght.