Anelka ensured the faltering Blues stayed in the hunt for silverware this season and eased the pressure on manager Carlo Ancelotti with a deadly double in Tuesday night's last-16 tie at the Parken Stadium, extending his remarkable scoring record in the competition to seven goals in six games.
Ancelotti defiantly declared on Monday, "Chelsea has not died", and Copenhagen proved the perfect opponents for a side who arrived in freezing Denmark with their season in danger of unravelling completely, the hosts clearly showing the effects of having not played a competitive match for two and a half months.
So while Tuesday night's victory was much-needed, the Blues will need to repeat it at home to Manchester United in the Premier League next week to demonstrate they are back on track.
They will also be concerned at another night to forget in front of goal for the recalled Fernando Torres, whose overall performance improved but who fluffed his chances against a side who were tailor-made for him to break his duck.
The home side's ring-rustiness was evident from the first minute, Torres too easily allowed to cross for Florent Malouda, who volleyed high and wide.
The heavy touch that dogged Torres at Fulham last week cost him an early chance to break his duck after Mathias Zanka was booked for wrestling him to the ground, Johan Wiland saving well at the striker's feet.
The £50million man began to settle, playing in Anelka for a shot that was blocked behind and showing more good touches.
There was minor panic in the Chelsea defence when Zdenek Pospech burst forward and saw a shot blocked and ricochet around the area.
But any nerves were calmed when their opponents gifted them a 17th-minute lead, former Stamford Bridge winger Jesper Gronkjaer of all people misplacing a pass straight to Anelka, who bore down on goal and calmly slotted past Wiland.
Torres lacked conviction when he tried to beat the last man and was again closed down by Wiland and also made a mess of a Frank Lampard through ball, while Anelka headed Malouda's cross over as Chelsea maintained their stranglehold.
The visitors were queuing up to score at times, Ashley Cole mis-controlling the ball on his chest when in acres of space six yards out and Anelka miscuing a left-foot strike straight into Wiland's arms.
Having wasted a hatful of chances in their previous two games, Chelsea knew a second goal could be crucial.
Torres was cautioned 10 minutes from half-time for tripping Cristian Bolanos before Anelka drilled over another decent opportunity.
Copenhagen tried to wrest the momentum by bringing on Martin Vingaard for Santin during the interval.
The new man made an immediate impact by forcing the first significant save from Petr Cech with a long-range strike.
He then curled straight into Cech's arms as the hosts began to show a determination almost completely absent during the first half.
But they were hit by a sucker-punch goal nine minutes in when a delightful first-time through ball from Lampard released Anelka, who drilled low across Wiland into the far corner.
Torres' misery in front of goal continued when he magnificently turned two defenders but sent his left-foot finish too close to Wiland.
Copenhagen's fans screamed for a penalty when Gronkjaer threw himself to the ground after turning Branislav Ivanovic but the flag was already up for offside.
The hosts' frustration boiled over when Pospech was booked bringing down Torres, ruling the defender out of the second leg.
Anelka left the field to a standing ovation from the visiting fans 16 minutes from time, as Drogba resumed his partnership with Torres.
The latter was again denied after superb skill from Malouda, his scuffed finish cleared off the line by Oscar Wendt, who was immediately withdrawn for Pierre Bengtsson.
N'Doye drilled wide from 25 yards and Vingaard and Claudemir fired straight at Cech from similar range as Copenhagen became increasingly desperate.
Malouda picked up a needless booking for time-wasting while leaving the field five minutes from time, Yury Zhirkov the substitute.
John Terry immediately followed for an unnecessary foul before Kenneth Zohore came on for Gronkjaer.
Michael Essien almost added a third Chelsea goal in the closing moments before Torres was replaced in stoppage-time by Salomon Kalou.