In his quieter moments Avram Grant has been known to reflect that he was lucky to end up as the first-team coach of Chelsea, although not half as fortunate as he remains in being able to call upon Didier Drogba.

With a typically powerful demonstration of his art, the Ivory Coast striker fired Chelsea into the knockout phase as group B winners last night, scoring two early goals to set them on course for a comfortable victory. Alex, the Brazilian who resembles an old-fashioned English defender, and Joe Cole, the Englishman who plays like a Brazilian, scored the others to finish off limited opponents in style.

Grant’s improved fortunes since he was putting out the cones at Portsmouth are not all down to luck, however, and the quietly-spoken Israeli deserves considerable credit for transforming a traumatised set of players into a team who have remained in contention in all competitions.

Chelsea have scored 30 goals in winning ten and losing only one of his 14 matches in charge – the first, at Old Trafford – while playing with greater freedom than they were afforded under José Mourinho. Greater challenges await, but Grant is confident enough to suggest that he could yet give Roman Abramovich a dream Champions League final in Moscow in May.

“This is one of our targets, maybe the main target, because we want to be a big club,” Grant said. “One of the things to achieve is to get to the final. I hope we will do it and we will do it.”

Given Drogba’s antipathy towards Grant’s appointment, it is a testament to the striker’s professionalism that he has recovered so quickly not only to stabilise but to strengthen a regime that looks capable of fighting for honours on all fronts. Drogba scored the surprise match-winning goal against Valencia last month that convinced many doubters of Grant’s credentials, so it was fitting that he should seal Chelsea’s qualification with another authoritative display.

Grant’s only concern was a jittery performance by Carlo Cudicini, whose poor positioning and vulnerability under crosses emphasised how important it is for Chelsea that Petr Cech recovers from a calf injury as soon as possible. Drogba was too hot to handle on a freezing night in Norway in a performance that underlined his case for individual honours.

The World Player of the Year award will be presented at a gala dinner in Zurich next month and although Fifa’s obsession with Champions League winners means that it will be won by Kaká, of AC Milan, Drogba deserves to feature in the top three. His dominance was all the more startling given that Vidar Riseth, the Norway centre back, had boasted beforehand of formulating a cunning plan to contain him after working with John Carew, the Aston Villa striker, on international duty; it proved to be as effective as one of Baldrick’s schemes.

“Didier is a very good striker,” Grant said. “We won without him [against Derby County on Saturday], but we wanted him to play. It’s easier with him in the side. It won’t be easy without him in January [when he will be at the African Cup of Nations], but we cannot change him.”

Grant had joked during the build-up to this match that his players would need to run around more than usual to combat the cold conditions and in an energetic opening they appeared to take him at his word. Chelsea could have opened the scoring on three occasions before Drogba finally did so in the eighth minute, with the Ivory Coast striker twice shooting wide before finding Michael Essien with an intelligent header from which he volleyed over the bar.

With Drogba at his rampaging best, it was only a matter of time before he was rewarded with a goal, although he was reliant on the brilliance of one of his teammates. After collecting the ball in his own half, Joe Cole embarked on one of those mazy runs that used to be his trademark before Mourinho stifled such creativity.

The England midfield player beat three opponents before unleashing a swerving shot from 25 yards that was saved by Lars Hirschfeld. Unfortunately for the former Tottenham Hotspur goalkeeper, he followed the example of one of his successors, Paul Robinson, by failing to clear the ball from the danger area and Drogba was on hand to sweep home from close range.

In this sort of mood, Drogba is unstoppable and he put the match beyond Rosenborg 12 minutes later. The 29-year-old had sought treatment for a back injury moments earlier, but he showed no ill-effects as he bundled home his ninth goal of the season.

Shaun Wright-Phillips found Essien in the penalty area and the Ghana midfield player held off two defenders, giving Drogba time to pounce with a left-foot finish. Chelsea’s dominance was such that they allowed Alex to score with a free kick in the 40th minute, before Cole added a fourth in the second half, to which Andriy Shevchenko, a substitute, even contributed. The Ukraine striker remains a peripheral figure under Grant, but many will seek to avoid his liberated team in the knockout phase.

How they lined up

Rosenborg (4-1-3-2): L Hirschfeld – F Stoor, B Kvarme, V Riseth, M Dorsin (sub: C Basma, 86min) – A Tettey, P Skjelbred, M Sapara, A Traoré (sub: R Strand, 56) – S Iversen, Y Koné (sub: D K Ya, 63). Substitutes not used: A Lund Hansen, M Koppinen, O Storflor, A Nordvik.

Chelsea (4-3-3): C Cudicini – J Belletti, Alex, J Terry, A Cole – M Essien, C Makelele, F Lampard (sub: C Pizarro, 77) – S Wright-Phillips (sub: S Kalou, 68), D Drogba (sub: A Shevchenko, 68), J Cole. Substitutes not used: Hilário, J O Mikel, W Bridge, T Ben Haim.