Andre Villas-Boas' side knew a defeat or scoring draw in this qualification shoot-out would put Valencia through at their expense, but two goals from Drogba either side of a Ramires strike eased Chelsea's path into the last 16.
Drogba's early goal settled any nerves and Ramires's strike midway through the first half put the Blues in a commanding position they never looked like squandering. Drogba netted again in the closing stages and there was even better news from Belgium where Genk held Bayer Leverkusen to allow Chelsea to leapfrog the Germans into top spot. That means Chelsea will avoid the likes of Barcelona, Real Madrid, Bayern Munich and Inter Milan in the draw for the next round.
"There has been a lot of criticism towards my players, but I think they gave everyone a slap in the face today," Villas-Boas said. "It's a fantastic result. I'm happy for the players because they worked very hard. And guess what? We finished top of the group against all odds!"
Drogba added: "There was a lot of pressure but you have to play until the last day of the group. Sometimes the pressure can be positive and it was today."
After a troubled start to his reign in West London, Villas-Boas had admitted the prospect of becoming the first Chelsea manager to see his side eliminated from the group stages of Europe's elite club competition was unthinkable. With that in mind, the boss took a major gamble by leaving England midfielder Frank Lampard on the bench and selecting Raul Meireles in his place.
His critics have already been sharpening their knives after Chelsea's spluttering run and Villas-Boas would have been lambasted if the Lampard move had back-fired. But Chelsea's 3-0 victory over Newcastle on Saturday had contained glimpses of the attacking style Villas-Boas employed so successfully at Porto and his decision to axe Lampard didn't affect the Blues' rhythm.
The thought of Thursday nights in the Europa League was clearly a substantial motivation for Villas-Boas's team and they made the perfect start as Drogba opened the scoring in the third minute. Daniel Sturridge swept a cross towards the far post where former Valencia winger Juan Mata expertly controlled before flicking the ball back to Drogba, who shifted the ball onto his left foot and drove a low shot past Diego Alves.
Valencia had no need to panic though as a draw would still send them through and they threatened an equaliser twice in quick succession. Spain left-back Jordi Alba made a well-timed run behind Branislav Ivanovic to slam a fierce shot against the near post. And the hosts were still recovering their composure from that narrow escape when Valencia midfielder David Albelda forced a superb diving stop from Petr Cech with a swerving 25-yard strike.
Just as Chelsea appeared to be rocking, they were gifted a second goal in the 22nd minute. Drogba embarked on a surging run down the left, but his pass towards Ramires should have been dealt with by Valencia defender Victor Ruiz. Instead, Ruiz made a tame attempt to nudge Ramires out of the way with his shoulder and the Brazil midfielder easily skipped around his opponent before poking the ball past Alves from close-range. Relief poured from the stands and the Chelsea dugout, where Villas-Boas leapt to his feet punching the air triumphantly.
Valencia had travelled to London in a rich vein of form, but the Spaniards looked overawed by the occasion for long periods. Unai Emery's team finally threw caution to the wind in the second half and Sofiane Feghouli tested Cech with a clever curling shot that the Chelsea keeper pushed away for a corner.
Villas-Boas responded by making a change, yet it was John Obi Mikel and not Lampard, who the Portuguese turned to when he replaced Ramires. Drogba was back to the bullish form that makes him such a handful and he sealed the win when he ran onto Mata's astute pass to slide a cool finish past Alves in the 76th minute.