James Forrest’s outstanding strike from a tight angle saw off a dogged Rosenborg side to secure Celtic’s place in the Champions League play-off round.
The visitors created the better opportunities in a goalless first half but had to survive a spell of Rosenborg pressure after the interval.
Celtic’s patience was rewarded when Forrest lashed the ball in from the right of the area after 69 minutes.
Rosenborg pushed forward in the final stages but could not break Celtic down.
The Scottish champions will face Astana, Qarabag, Rijeka, Hapoel Beer Sheva or Slavia Prague in the play-off round, with Kazakh side Astana and Israel’s Hapoel having lost to Celtic in last year’s competition.
Celtic manager Brendan Rodgers had opted for an element of caution, leaving the fit-again Leigh Griffiths on the bench and starting winger Forrest as a makeshift central striker.
Erik Sviatchenko returned to the starting line-up, but lasted only 24 minutes before injury forced him off. Celtic endured the setback, though, and eventually prevailed, with Forrest spurning a one-on-one with the goalkeeper late on to increase the lead.
The Scottish champions created few chances in the home leg, but Rodgers was confident his side would benefit from an extra week’s training as they try to rediscover the devastating attacking fluency of so much of last season’s play.
Kieran Tierney was certainly prominent early on as a threat down the left, surging forward from his full-back role, and one drilled cross presented an opportunity to Forrest, whose effort was tipped over by Rosenborg goalkeeper Andre Hansen.
Celtic’s best other effort came from a set piece, with Jonny Hayes slinging over a cross that Sviatchenko headed on target only for his Danish compatriot Nicklas Bendtner to block the ball on its way to the goal-line.
Rosenborg tried to prompt and probe in the final third when they could make ground forward, but all that Celtic goalkeeper Craig Gordon had to cope with was a weak long-range effort by Milan Jevtovic.
The home side were more assertive after the interval, though, noticeably closing the Celtic players down more urgently. The change in approach was effective, since they enjoyed a spell of pressure.
Celtic mostly stood firm, but Bendtner was a threat and showing a deft touch with his chest, he steered a high ball cleverly into the path of Yann-Erik de Lanlay, who pulled his shot beyond the far post.
Needing to alter the dynamic of the game, Rodgers replaced Hayes with Griffiths, hoping that the centre forward and proven scorer would provide a cutting edge to his side.
Bendtner continued to show more willingness to be involved, and another intervention led to Mike Jensen’s shot just brushing the outside of the post.
Rosenborg’s menace would have been a concern for Celtic, but the visitors played with maturity and continued to rely on their self-belief; it was eventually rewarded.
Sinclair burst through the middle to the edge of the area then moved the ball out to Forrest on the right, who skipped past his marker then lashed the ball high past Hansen from a tight angle, the ball crashing in off the underside of the bar.
It was the breakthrough that Celtic craved, and enough to secure a deserved place in Friday’s play-off round draw.