Rosenborg threatened to spring a surprise when Miika Koppinen turned in Marek Sapara's free-kick at the near post in the 24th minute.
Florent Malouda and Salomon Kalou hit the woodwork for Chelsea, but resilient Rosenborg held out to force a draw.
And perhaps even more worrying for coach Jose Mourinho was a crowd of only 24,973 at Stamford Bridge, including a distinctly unimpressed owner Roman Abramovich - a miserable turn-out for a Champions League game.
Mourinho told ITV4: "I think they were not a problem, we were the problem because it's a game you can win (by) five, six or seven. A team that can produce, produce, produce but doesn't put the ball in the net.... this is what football is about.
"(Rosenborg) defended, they tried to do things on the counter-attack. They did their game, and if i was in their place I would do the same. You have to use your ammunition, so I'm not criticising. I congratulate them."
