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 their chances against their second-tier opponents but could not take their opportunities and now have their work cut out to avoid exiting at the first hurdle for the fourth year in a row.
Irish League Cliftonville gave themselves 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, who reached the quarter-finals of the UEFA Champions League 15 years ago.
The Norwegians, featuring former Tottenham striker Steffen Iversen in their 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 hosts two up inside the first 20 minutes, but Jason Bowen gave the Welshmen hope in first half injury time.
Cefn Druids marked the first European game in their history with a goalless draw against Finnish side MyPa at Wrexham's Racecourse Ground, while Bangor City were also held 0-0 at home by Moldovan side Zimbru.
Hibernian, meanwhile, went down 5-2 to FK Sarajevo.