Rosenborg threatened to spring a surprise when Miika Koppinen turned in Marek Sapara's free-kick at the near post in the 24th minute.
Andriy Shevchenko headed Chelsea level eight minutes after the interval.
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."