Linfield went down narrowly to Vikingur of the Faroe Islands in the first leg of their third round Conference League qualifying clash, while Larne have more of a mountain to climb as they slumped to a 3-0 defeat at home to Portuguese side Santa Clara.
The outcome of both ties could yet be significant for both Shelbourne and Shamrock Rovers. If Joey O'Brien's side lose out to Rijeka in their Europa League third round encounter, they will then face the winner of Linfield/Vikingur in the play-off round.
The Hoops, who trail Ballkani by 1-0 ahead of the return leg in Tallaght Stadium, looked poised, as things stand, to face Santa Clara if they can get the better of their Kosovan opponents.
Vikingur took an early lead through a third-minute own goal from Blues defender Ben Hall before Matthew Fitzpatrick swiftly headed in an equaliser.
Left-back Ingi Jonhardsson fired home an angled drive in the 55th minute to give the Faroe Islanders a slender first-leg advantage.
Santa Clara were the dominant side at the Ballymena Showgrounds, where Gabriel Silva scored twice in the first half for the visitors.
