Last year's beaten semi-finalists dominated the game from start to finish but could find the back of the net only once through Andriy Shevchenko's first goal of the season.
Jose Mourinho's side had fallen behind to Miika Koppinen's 24th minute opener as the Norwegian champions broke the deadlock with virtually their first attack of the match.
Chelsea were once again unable to call upon the services of the Didier Drogba (knee) and Frank Lampard (thigh), while Peru striker Claudio Pizarro (calf) was also ruled out.
And the absence of the key trio was obvious as the Blues enjoyed the lion's share of possession but failed to turn it into goals.
Salomon Kalou mistimed a close-range 10th minute header which dropped onto the roof the net, before Florent Malouda's side-foot shot was cleared from close to the line by Christer Basma as the home side dominated the opening period.
But Rosenborg weathered the early storm and took a shock lead in the 24th minute.
Marek Sapara delivered a tantalising cross from the left wing and Koppinen volleyed the ball home from close range ahead of Petr Cech.
That moment should have sparked Chelsea into life but Kalou and Shevchenko were both off-target with difficult chances in the build up to half-time.
Chelsea continued to hold the upper hand after the interval and, with Mourinho increasingly prowling the technical area visibly unhappy with his side's display, they pulled themselves back on level terms after 53 minutes.
Malouda was given all the time in the world to deliver a cross and Shevchenko nipped in ahead of Koppinen and goalkeeper Lars Hirschfeld to head bravely home from six yards.
Malouda almost turned from provider to scorer ten minutes later when he rattled the upright with a stinging low shot from the corner of the box as Chelsea looked for the winner.
But, when Kalou also hit the upright after looking to pick his spot past the keeper 13 minutes from full-time, it looked like it might not be Chelsea's night.
Kalou also saw a close-range shot blocked by two desperate defenders in the final minutes as a sometimes ponderous Chelsea ran out of ideas in an ultimately disappointing display.