Top-three finish only target left for Rovers
Odds BK 2 Shamrock Rovers 1, Odds BK win 4-1 on aggregate
Late strikes from Ole Jorgen Halvorsen and Steffen Hagen were more than sufficient for Odds BK to end Shamrock Rovers' Europa League hopes at the Skagerak Arena.
Gavin Brennan reduced the deficit in the last minute but that provided little consolation for the Hoops, whose only realistic goal for the rest of the season is to finish in the top three and so qualify to play in Europe again next season.
Rovers craved the first goal of this second leg tie, but in truth it never looked like coming their way as a measured Odds performances saw the Norwegians comfortably through to meet Elfsborg of Sweden in the third qualifying round.
Rovers' manager Pat Fenlon made one change from the first leg, with Brandon Miele returning to the side and Marty Waters dropping to the bench.
In a surprise move by Odds boss Dag-Eilev Fagermo, Canadian international striker Olivier Occéan, who scored both goals in last week's 2-0 first leg win, and key midfielder Jone Samuelsen were rested with Sunday's Tippeligaen game at home to Tromso in mind.
Save for an even opening period when Ryan Brennan headed wide from a Gary McCabe free kick, Odds dominated the first half, Rovers' first scare arriving on 14 minutes.
Halvorsen broke on the right to feed Oliver Berg whose low pull-back was well cut out by Luke Byrne. Simon Madden then produced a timely interception to deny Rafik Zekhnini before Chukwuma Akabueze blasted a drive straight at Craig Hyland.
With Occéan on from the start of the second half, Odds should have been two goals up within five minutes of the resumption.
After a shout for a handball by Rovers at one end was ignored, Odds quickly broke and Halvorsen's cross was somehow scooped over the bar by Zekhnini. Berg then also contrived to blaze his shot over the top from close range.
A loose back-pass at the other end gifted Cregg a sight of goal, but his scuffed shot was comfortable for Sondre Rossbach, who then made a smart save to deny Mikey Drennan.
Odds made the breakthrough on 71 minutes. Byrne's weak header was picked up by Samuelsen who skipped to the end line and delivered a cross which Halvorsen drilled home.
Hagen added the second after 85 minutes with a powerful back-post header form Espen Ruud's corner.
Rovers' replay came right on 90 minutes. Madden's deep cross from the right was knocked back by Danny North for Gavin Brennan swept the ball home close range.
ODDS BK - Rossbach; Ruud, Eriksen (Bergan, 78), Hagen, Jonassen; Berg, Gashi, Nordkvelle (Samuelsen, 62); Halvorsen, Akabueze (Occéan, h/t), Zekhnini.
SHAMROCK ROVERS - Hyland; Madden, Kenna, Webster, Byrne; McCabe, Cregg (C Kavanagh 67); Miele (North 80), R Brennan, G Brennan; Drennan.
REF - M Avram (Romania).