Dundalk defeated KI Klaksvík 3-1 in Dublin to reach the Europa League group stage and secure a financial windfall in the region of £2.7m.
Goals either side of half-time from Sean Murray and Dan Cleary gave the League of Ireland side a two-goal lead.
Ole Midtskogen pulled a goal back for the Faroese outfit on 66 minutes before substitute Daniel Kelly sealed victory for the Lilywhites.
It is only the third time an Irish club has qualified for the group stage.
Shamrock Rovers made it through to that stage of the Europa League in 2011 and Dundalk themselves did the same in 2016, when current Republic of Ireland manager Stephen Kenny was in charge.
The match was taking place in Dublin's Aviva Stadium as Dundalk's Oriel Park ground did not meet the Uefa specifications for hosting the tie.
The Premier Division title holders have struggled in the league this season and manager Vinny Perth was sacked when they lost 3-0 to Slovenian side NK Celje in the Champions League first qualifying round.
Little-known Italian Filippo Giovagnoli was appointed by the club's US owners and guided them past Inter d'Escaldes of Andorra before a penalty shootout win over Sheriff Tiraspol in Moldova brought them to Thursday night's encounter.
As well as the £2.7m that qualifying for the Europa League group stage guarantees, each win thereafter would secure in the region of £520,000 with approximately £170,000 added to the pot for draws.
Murray's opener came in the 33rd minute from a deep Sean Hoare cross that was headed on by Patrick Hoban, with midfielder Murray getting in ahead of goalkeeper Kristian Joensen to head home from close range.
Giovagnoli's men doubled their advantage three minutes after the restart when Joensen flapped at a Michael Duffy corner, with the ball deflecting off Huban into the path of Cleary who lashed home.
Duffy came close with a good run and shot before but the visitors responded well and twice went close before pulling a goal back on 66 minutes.
Joannes Bjartalid fed Midtskogen with a neat lay-off and the midfielder hammered home a low shot from 22 yards that took a slight deflection before going past keeper Gary Rogers.
KI were pressing for an equaliser when Dundalk broke quickly for the third goal 11 minutes from time, Murray feeding Kelly who took a super first touch before slotting into the bottom corner.
The Faroese did not give up but Dundalk stood firm to make it through.
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- 7JohannesenBooked at 82mins
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- Maurizio Mariani
- Shots on Target