Chris Fagan's 39th-minute goal gave St Patrick's Athletic hope of progressing past the first preliminary round of the UEFA Europa League with a 1-0 win over IBV in Dublin.
Fagan finished off a cross from Ger O'Brien to give Liam Buckley's men a slender advantage heading into the second leg in Iceland next week.
The League of Ireland side will travel with confidence having beaten IBV at the same stage last season, overturning a 1-0 first-leg deficit to triumph 2-1 on aggregate.
But there was frustration across Dublin as Bohemians had to settle for a goalless draw against another Icelandic side, Thor, at Dalymount Park.
Bohemians fancied its chances against its second-tier opponent but could not take its chances and now has its work cut out to avoid exiting at the first hurdle for the fourth year in a row.
Irish League Cliftonville gave itself a good chance of making the next round with a 1-0 win over Allsvenskan side Kalmar in Belfast. Liam Boyce struck the only goal in the 71st minute.
But Crusaders predictably found the going too tough against Norwegian side Rosenborg, which reached the quarter-finals of the UEFA Champions League 15 years ago.
The Norwegian side, featuring former Tottenham striker Steffen Iversen in its starting line-up, cantered to a 3-0 win with two goals from Mikael Dorsin and one for Borek Dockal.
Crusaders had Declan Caddell sent off in the 74th minute.
League of Wales side Llanelli snatched a potentially crucial away goal in a 2-1 defeat to KuPS in Finland. Markus Joenmaki and Ats Purje put the host two up inside the first 20 minutes, but Jason Bowen gave the Welsh side hope in first half injury time.
Cefn Druids marked the first European game in its history with a goalless draw against Finnish side MyPa at Wrexham's Racecourse Ground, while Bangor City was also held 0-0 at home by Moldovan side Zimbru.