Celtic set up a tie with AEK Athens by eliminating Rosenborg in the Champions League second qualifying round.
A goalless draw in Trondheim meant Celtic's 3-1 first-leg win was sufficient to beat the Norwegians.
The hosts dominated the first 45 minutes, Marius Lundemo having a powerful header saved by Craig Gordon with the best chance of the half.
Celtic were much better after the break, Odsonne Edouard and Scott Sinclair coming closest to scoring.
Tore Reginiusses was denied a late goal when he was adjudged to have fouled Gordon as the two contested an aerial ball.
Brendan Rodgers' men will host AEK Athens next Wednesday, with the return leg taking place in Greece the following week.
Rosenborg drop into the Europa League third qualifying round, where they will face Cork City.
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Blunt Rosenborg spare Celtic
This was not vintage Celtic, but as Rodgers had underlined pre-match, the task so early in the campaign is finding a way to progress.
Rosenborg were tidy, but blunt in ****** – mercifully for Celtic. They enjoyed the bulk of the first-half possession and pressure, but scarcely made it tell.
Gordon did have to make one vital intervention in injury time, springing upwards and pushing Lundemo's looping header over the bar.
Otherwise, his contributions were limited to dealing with a couple of inswinging corners and making a meal of a hopeful cross from the dangerous Pal Andre Helland.
Celtic looked to be playing well within themselves. The onus was not on them to take the initiative and it was not until the opening minute of the second period that they threatened a potentially decisive away goal.
Edouard combined down the left with Callum McGregor before deftly gliding away from two defenders, only to curl his shot narrowly wide.
Celtic began to take greater care of the ball, presumably something demanded of them by their manager at the break.
But substitute Jonathan Levi injected life into the home side and he stung the palms of Gordon with a fierce shot from the right of the penalty area.
Celtic still have several first-team players working their way to full fitness and will be in a better place when AEK Athens visit Glasgow. They will probably have to be too.
'Wholesale improvements needed for AEK' – analysis
Former Celtic goalkeeper Pat Bonner on BBC Radio Scotland:
I want to see Celtic coming to these places and controlling the game. In that first half, they just didn't.
They'll have to improve against these higher-level teams, like AEK. They will create things around the edge of the box, they will be quick and sharp in bursts, and Celtic will have to defend better against that.
Former Celtic striker Scott McDonald on BBC Radio Scotland:
Rodgers will still be disappointed, but they were comfortable. I can't really think of too many chances that Rosenborg had. I think they just ran out of ideas.
The job was done in the first leg. They will just have to be more aware against AEK, sharpen up defensively and make sure they are more compact. The first leg is at Celtic Park and if they perform as they did against Rosenborg, they will be in good shape.
- 3MelingBooked at 8mins
- 25LundemoSubstituted forBotheimat 90+2'minutes
- 15TrondsenSubstituted forVilhjálmssonat 75'minutes
- 23HellandSubstituted forLeviat 58'minutesBooked at 74mins
- 21Dahl Reitan
- 35AjerBooked at 88mins
- 63TierneySubstituted forLustigat 85'minutes
- 49ForrestSubstituted forRogicat 63'minutes
- 22EdouardSubstituted forChristieat 72'minutes
- Sandro Schärer
Match ends, Rosenborg 0, Celtic 0.
Second Half ends, Rosenborg 0, Celtic 0.
Substitution, Rosenborg. Erik Botheim replaces Marius Lundemo.
Kristoffer Ajer (Celtic) is shown the yellow card for a bad foul.
Substitution, Celtic. Mikael Lustig replaces Kieran Tierney.
Substitution, Rosenborg. Matthías Vilhjálmsson replaces Anders Trondsen.
Jonathan Levi (Rosenborg) is shown the yellow card for a bad foul.
Substitution, Celtic. Ryan Christie replaces Odsonne Edouard.
Substitution, Celtic. Tomas Rogic replaces James Forrest.
Substitution, Rosenborg. Jonathan Levi replaces Pål Helland.
Second Half begins Rosenborg 0, Celtic 0.
First Half ends, Rosenborg 0, Celtic 0.
Birger Meling (Rosenborg) is shown the yellow card for a bad foul.
First Half begins.
Lineups are announced and players are warming up.