Carlo Ancelotti's side are now ahead of Spartak Moscow on goal difference after the Russians defeated MSK Zilina 3-0 earlier today.
Marseille, managed by former Chelsea player Didier Deschamps, now face a real struggle to qualify for the knockout stage of the competition.
Chelsea went into their Group F game on the back of two successive defeats to Newcastle in the Carling Cup and Manchester City in the Premier League.
Deschamps had called for his side to show the same physical prowess and counter-attacking guile that City used to overcome the Blues at Eastlands on Saturday.
But his plan went awry when Chelsea took the lead in the seventh minute with their first real attack of the game.
Florent Malouda's shot was deflected for a corner and when Gael Kakuta aimed it at the near post, captain Terry stole in to flick the ball home.
It was a dream start for the English champions and it could have been better in the 13th minute had Malouda been able to prevent his 10-yard shot from going just over the Marseille crossbar.
Anelka, who was roundly booed by Marseille fans from the kick-off, brought a fine save from Steve Mandanda moments later after Kakuta's ball had sent him racing in on goal.
Chelsea's night got even better in the 27th minute when Stephane Mbia was harshly adjudged to have handled Michael Essien's attempted cross.
The Marseille defender was booked for the misdemeanour and Anelka rubbed salt into their wounds by tucking away the resultant spot-kick with ease.
Anelka was a constant thorn in the side of Marseille and he was just a yard away from grabbing his second in the 42nd minute when he tried his luck from 20 yards.
Marseille had barely troubled Chelsea goalkeeper Petr Cech in the opening period but the French champions picked up the pace after the restart.
Andre-Pierre Gignac, who had been largely kept well marshalled by Terry and Alex, sent an overhead kick straight at Cech.
In the 57th minute, Brandao tested Cech's readiness with a 25-yard effort that the Czech Republic international did well to hold on to.
Marseille replaced Gignac and Benoit Cheyrou with Andre Ayew and Mathieu Valbuena moments later as they looked for a way back into the contest.
Chelsea reacted to Marseille's changes swiftly with coach Carlo Ancelotti opting to replace Kakuta with Ramires on the hour.
Ashley Cole and Terry then combined to keep out a fierce shot from Souleymane Diawara.
Chelsea went close to adding a third in the 67th minute but a fantastic 35-yard free-kick from Alex hit the inside of the post with Marseille goalkeeper Mandanda well beaten.
Essien was guilty of hitting the right-hand upright in the 75th minute when Chelsea opened-up Marseille with another move of fluid simplicity.
Malouda fed Ramires in the inside-left channel and the Brazilian calmly laid the ball into the path of the onrushing Essien.
But the man nicknamed 'the Train' sent his thunderous right-foot shot against the upright.
Chelsea removed Yury Zhirkov in favour of Daniel Sturridge and the youngster was later joined by teenager Josh McEachran, who replaced John Obi Mikel.
Moments later Sturridge squandered a simple chance to score when Anelka and Cole combined superbly down the left flank to provide him with the opportunity.
Sturridge met Cole's cross on the edge of the six-yard box but somehow managed to turn the ball beyond the far post.
In the 89th minute Essien was narrowly wide when Cole picked him out on the edge of the penalty area.
The Ghanaian looked to have done everything right but his left-foot effort spun inches beyond Mandanda's right-hand post.
It was the last chance of a game Chelsea had bossed throughout to leave them top of the group with a trip to Moscow looming in a fortnight.