Anders Konradsen headed in on 20 minutes and the striker made it 2-0 with a volley early in the second half.
Substitute David Akintola added the third with a close-range finish and Pal Andre Helland fired in at the near-post to complete a comfortable win.
Irish League winners Linfield drop into the Europa League qualifiers.
David Healy’s side will make the trip to the Faroe Islands to take on HB Torshavn in the second-round first leg next Tuesday.
A 2-0 defeat in Belfast last week left the Blues with a huge task at the Lerkendal Stadion and despite a brave effort they were once again outclassed by the Norwegians.
Shayne Lavery, Chris Chrisment and Jordan Stewart had first-half efforts for the visitors but the main danger came at the other end.
Konradsen got on the end of Vegar Hedenstad corner for the opener while Helland hit the side-netting and Yann-Erik de Lanlay volleyed over.
Matthew Clarke rifled over for the Blues on the restart before Konradsen struck again with his scissor-kick finish bouncing high into the net from a Helland cut-back on 50 minutes.
A defensive blunder let in the hosts for their third – goalkeeper Gareth Deane blocked a shot after his pass out was intercepted, but the ball ballooned up to give Akintola a simple finish after 69 minutes.
The impressive Helland, who had earlier struck the bar from a free-kick, tucked home the fourth from Akintola’s pinpoint cross.
Rosenborg’s reward is a second-round Champions League qualifier against BATE Borisov or Piast Gliwice.
- 2Eggen HedenstadSubstituted forTrondsenat 45′minutes
- 8KonradsenSubstituted forKonradsen Ceideat 71′minutes
- 11de Lanlay
- 14SøderlundSubstituted forAkintolaat 58′minutes
- 35Konradsen Ceide
- 10StewartSubstituted forMillarat 74′minutes
- 3LarkinBooked at 63mins
- 14LaverySubstituted forWaterworthat 58′minutes
- 47CasementBooked at 39mins
- 22MulgrewBooked at 42minsSubstituted forFallonat 59′minutes
- Enea Jorgji
Match ends, Rosenborg 4, Linfield 0.
Second Half ends, Rosenborg 4, Linfield 0.
Goal! Rosenborg 4, Linfield 0. Pål André Helland (Rosenborg) right footed shot from the centre of the box to the centre of the goal.
Substitution, Linfield. Kirk Millar replaces Jordan Stewart.
Substitution, Rosenborg. Emil Konradsen Ceide replaces Anders Ågnes Konradsen.
Goal! Rosenborg 3, Linfield 0. Babajide David Akintola (Rosenborg) right footed shot from the centre of the box to the centre of the goal.
Ross Larkin (Linfield) is shown the yellow card for a bad foul.
Substitution, Linfield. Stephen Fallon replaces Jamie Mulgrew.
Substitution, Rosenborg. Babajide David Akintola replaces Alexander Søderlund.
Substitution, Linfield. Andrew Waterworth replaces Shayne Lavery.
Goal! Rosenborg 2, Linfield 0. Anders Ågnes Konradsen (Rosenborg) right footed shot from the centre of the box to the centre of the goal.
Substitution, Rosenborg. Anders Trondsen replaces Vegar Eggen Hedenstad.
Second Half begins Rosenborg 1, Linfield 0.
First Half ends, Rosenborg 1, Linfield 0.
Jamie Mulgrew (Linfield) is shown the yellow card for a bad foul.
Chris Casement (Linfield) is shown the yellow card for a bad foul.
Goal! Rosenborg 1, Linfield 0. Anders Ågnes Konradsen (Rosenborg) right footed shot from the centre of the box to the centre of the goal.
First Half begins.
Lineups are announced and players are warming up.