The Norwegian side, domestic champions for 13 successive seasons before finishing seventh in 2005, remain in contention to join Avram Grant's side in the knockout stages of the competition thanks to their two wins against Valencia.
But they were a well-beaten side on the night thanks largely to Chelsea's dynamic start.
Ten weeks ago the west London side were held to a 1-1 draw by Rosenborg at Stamford Bridge and within 24 hours Jose Mourinho was heading out of the club.
For a time it looked as though Chelsea would fall apart, but fast forward to late November and the Blues appear as strong as ever.
After Drogba had twice gone close to opening the scoring and Michael Essien had fluffed a golden chance, it was the Ivory Coast international who broke the deadlock in the seventh minute.
The outstanding Joe Cole ended a fine run with a rasping shot that Rosenborg keeper Lars Hirschfeld could only push out to Drogba and he wasted no time lashing the ball into the roof of the net.
In a lively opening John Terry gifted the ball to Steffen Iversen with a poor header and the former Tottenham man set up Marek Sapara, whose shot was fumbled by Carlo Cudicini before the keeper grabbed the ball at the second attempt.
However, in the 20th minute it was 2-0 to Chelsea. Shaun Wright-Phillips surged towards the penalty area and found Essien and, although the Ghanaian was crowded out, the ball fell to Drogba who drilled his shot home.
On the half-hour Frank Lampard tried to get in on the act by attempting a cheeky chip, but Hirschfeld was able to back-pedal and grab the ball above his head.
However, the match was won five minutes before the interval with a bizarre goal.
Alex's ambitious free-kick was poorly struck, but it somehow went through the wall and past Abdoulrazak Traore's outrageous attempt to stop the ball before nestling in the net beyond Hirschfeld.
Chelsea continued to dominate after the break as the Norwegians threatened to be over-run. Wright-Phillips fired against the crossbar in the 53rd minute before Essien's effort was somehow scrambled off the line by the over-worked Rosenborg defence.
The hosts' best chance of a consolation goal came in the 67th minute when Cudicini did well to tip Sapara's free-kick over the bar.
However, the Blues completed the rout six minutes later when Joe Cole was first to react after Essien's shot had been parried by Hirschfeld and the England man prodded the rebound into an empty net.