Christy Fagan ensured St Patrick's Athletic will bring a 1-0 Europa League first qualifying round lead with them to Iceland when they face IBV in the second leg next week.
Fagan's 38th minute strike means that Pat's will head for Iceland heartened as IBV failed to score an away goal.
The early stages offered real encouragement for the Saints, who were passing the ball with typical precision.
Throughout this campaign Liam Buckley has opted for a 4-3-3 formation and it ensured the Dubliners enjoyed plenty of possession.
James Chambers sat in front of the defence with John Russell and Greg Bolger afforded licence to drive forward to support Christy Fagan.
It was certainly working initially as Pat's were quickly on the front foot and they carved an opportunity in the sixth minute.
Seanie O'Connor, clever on the left flank, exchanged passes with Ian Bermingham, but the winger's shot was deflected out for a corner.
But then against the run of play IBV went close to nicking the lead as the Saints survived a significant scare.
Christian Olsen connected with a Matt Garner delivery, but the ball shaved the crossbar and Pat's rode their luck.
A physical IBV outfit also displayed flair in the 20th minute when a splendid move featuring Brynjar Gudjonsson and Ian Jeffs ended with Conor Kenna making a crucial block to deny Tryggvi Gudmundsson.
Still, Pat's were creating chances at the opposite end too and moments later IBV custodian Abel Dihara had to be alert to save a long-range O'Connor effort.
Ten minutes before the break a Darren Meenan corner caused panic in the IBV area, but Kenny Browne was unable to direct his header on target.
The Saints netted, though, in the 38th minute as a crunching James Chambers challenge ensured Ger O'Brien was able to rifle a sweet cross in from the right.
Christy Fagan timed his run expertly and was sufficiently crafty to nudge the Dubliners ahead with an opportunistic finish.
In the third quarter there was surprisingly little goalmouth action as Pat's struggled to attain the same passing fluency.
Substitute Dean Kelly had a shot saved by Dihara in the closing stages as the Saints held on for a satisfying success.