Sean Murray, Daniel Cleary and Daniel Kelly hit the net for the hosts, who were never overly troubled by their Faroe Islands foes.
Ole Erik Midtskogen found the net for Klasvik but Dundalk eased through the qualifying rounds.
Harry Kane’s hat-trick fired Tottenham into the Europa League group stages with a 7-2 win over Maccabi Haifa in north London.
Giovani Lo Celso bagged two goals in three minutes as Jose Mourinho’s Spurs overwhelmed their Israeli visitors at the Tottenham Hotspur Stadium.
Lucas Moura was on target too, before Dele Alli converted a penalty in added time.
FULL-TIME: A dominant night at Tottenham Hotspur Stadium sees us book our place in the @EuropaLeague Group Stages!
⚪️ #THFC 7-2 #MHFC 🟢 pic.twitter.com/e32tP1ITXG— Tottenham Hotspur (@SpursOfficial) October 1, 2020
Tjaronn Chery and Nikita Rukavytsya hit back for Maccabi, but the travelling team were overwhelmed by Mourinho’s men.
The win puts Spurs into the hat for Friday’s group stage draw, which takes place at UEFA’s Nyon headquarters in Switzerland.
Odsonne Edouard prodded home midway through the second half to hand Celtic safe passage to the group stage shake-up, as Neil Lennon’s men won 1-0 at FK Sarajevo.
Goalkeeper Vladan Kovacevic spilled Ryan Christie’s shot, allowing Edouard the opening to notch the winner.
Full-back James Tavernier fired his seventh goal in as many games as Rangers overcame Galatasaray 2-1 at Ibrox.
Steven Gerrard’s men reached the last 16 of Europe’s second-tier tournament last term, and were in no mood not to reach the competition-proper this time around.
Scott Arfield found the net just three minutes after the opener as Rangers took control just ahead of the hour, with Tavernier again influential in neat build-up also involving Alfredo Morelos and Ianis Hagi.
Marcao’s late header put the jitters into the hosts, but Gerrard’s men held on.
