The Icelandic substitute rose highest to meet Vegar Hedenstad’s 98th minute cross to put Kare Ingebrigtsen’s side ahead for the first time in the tie.

However, only the width of the woodwork denied Dundalk a dream clash with Celtic in Glasgow next week as goalkeeper André Hansen tipped Ciaran Kilduff’s shot onto the bar in stoppage time at the end of the half.

Had that gone in Dundalk, like they did against FH Hafnardjordur at this stage last season, would have advanced on away goals.

While they were forced to weather the storm for long periods of the game, it would not have flattered Stephen Kenny’s men after they put in a superb showing.

They were briefly in dreamland when captain Brian Gartland gave them an early lead but the home side responded with a goal through Yann-Erik de Lanlay just before half-time to leave things incredibly tense for the remaining 77-plus minutes in Trondheim.

Vilhjalmsson’s goal was a blow but Dundalk kept pressing afterwards for a winner. Unfortunately it just eluded them and so there will be no repeat of last season’s stunning European adventure.

Just like in the first leg the Louth men got off to a fantastic start with the opening goal from the game’s first attempt on 12 minutes.

A great ball out of defence from Niclas Vemmelund saw him release John Mountney on the right with the winger winning a corner off Birger Meling. Michael Duffy’s delivery then saw Gartland get up above Jorgen Skjelvik with his downward header into the ground creeping past Hansen to the left hand corner.

It could have been 2-0 for Dundalk just three minutes later when another Duffy corner saw David McMillan get a header away that had to be touched over the bar by Hansen.

Rosenborg were visibly rattled at this point with Skjelvik almost turning the ball into his own net in the 20th minute.

The Norwegians finally began to exert some pressure in the closing third of the half though as the visitors began to drop deeper than their manager would have liked.

Despite that it took until the 42nd minute for them to cut through the Lilywhites when Hedenstad was slipped in on the right by Fredrik Midtsjo but Vemmelund did brilliantly to get across to block the effort.

Within a minute Rosenborg had their equaliser. Captain Mike Jensen turned broke from midfield before slipping de Lanlay in behind Sean Gannon on the left to slot past the advancing Rogers.

Rocked by the concession, Dundalk were perhaps fortunate not to concede a second before the break when Midtsjo’s mishit shot fell to the feet of Milan Jevtovic whose shot had to be clawed around the post by Rogers.

Midtsjo again threatened within a minute of the restart when he worked space for himself to get a shot away but once again Vemmelund was on hand to block his effort.

Dundalk were by now heavily on the backfoot and had another major let-off on 69 minutes when Tore Reginiussen almost scored an identical goal to his first leg equaliser. The centre half was picked out unmarked at the edge of the six yard box by Hedenstad’s free kick but on this occasion he could only slice his effort into the grateful arms of Rogers.

Having weathered the storm, Dundalk began to grow into the game and on 83 minutes a clever free kick routine saw a combination of Patrick McEleney and Stephen O’Donnell tee up Robbie Benson from a free kick which Hansen had to turn around the post.

Both sides then had chances at the death to prevent extra-time with McMillan heading a Dane Massey cross wide before Rogers turned a Midsjo shot around the post in the first minute of stoppage time.

Rosenborg’s pressure continued into extra-time with Skjelvik drilling just wide moments before Vilhjalmsson headed the hosts in front.

The Norwegians had goalkeeper Hansen to thank for keeping them in the game, however, when he topped Kilduff’s effort from Gartland’s flick on onto the top of the crossbar in stoppage time.

There was a couple of half chances in the second half for Kilduff and Jamie McGrath but neither seriously threatened Rosenborg as the Irish champions’ challenge simply ran out of steam.

The dream is over for Dundalk and it’s one they will rue letting slip for some time to come.

Rosenborg: Hansen, Hedenstad, Reginiussen, Skjelvik, Meling; Jensen, Konradsen, Midtsjo, Jevtovic, Bendtner (Lundemo 114), de Lanlay (Vilhjalmsson 72).

Dundalk: Rogers; Gannon, Gartland, Vemmelund, Massey; Mountney, Benson, Shields, Duffy (O’Donnell 59); McEleney (McGrath 84); McMillan (Kilduff 94).

Referee: Aliyar Aghayev (Azerbaijan).