Drogba's expertly dispatched strike was a desperately disappointing denouement for Liverpool, who had looked in command of this match.
With Steven Gerrard and Dietmar Hamann models of industry in midfield, Liverpool had taken control with Milan Baros's fine piece of poaching shortly after the break.
But loose defending late on, granting Drogba a glimpse of goal, has complicated Liverpool's hopes of reaching a quarter-final with either Benfica or Inter Milan.
The UEFA Cup may be the B-road that winds through Europe but there are enough A-list names in the frame to embellish the competition with residual appeal, not least seven past winners of the European Cup.
One of them, Marseilles, certainly deserved the respect of Liverpool, four times kings of Europe, although the visitors' sound organisation and clever tactical game plan was dented when the excellent Baros pounced 10 minutes after the break.
Until then Liverpool had been finding it hugely difficult to negotiate their way through the maze that was the Marseilles midfield. The French had flooded the centre, hoping to stymie Gerrard (in vain, as it proved) and leaving Steve Marlet to shuttle back and forth while the muscular, lively Didier Drogba carried the game to Liverpool's defence.
Drogba, attacking the Kop and giving Sami Hyypia a thoroughly awkward night, had clearly taken the Liverpool fans at their word, responding hungrily to a marvellous mosaic of cards forming the word allez in honour of Houllier.
The Marseilles No 11 was a constant irritant, even having a brief contretemps with Baros following a foul on Fabien Barthez, the Marseilles goalkeeper. Drogba menaced most when running at Hyypia and company rather than when shooting from range; one of his 25-yarders trickled through almost apologetically to Chris Kirkland.
The French were the more impressive through a disappointing, scoreless first half. Until the second half brought a quickened pace from Liverpool there had been little to entertain Anfield, barring the opportunity to boo Barthez for his Manchester United connections. When Barthez ran out for the second half to take his place in the Kop goal, he was greeted with a squadron of paper darts.
Moments did begin to arise. After 24 minutes Danny Murphy teased the ball left to Harry Kewell, whose cross was met by Michael Owen. As Anfield stood in expectation Owen's response lacked conviction, the England striker shooting weakly at Barthez.
Owen was presented with another chance just before the interval courtesy of a quickfire interchange between Gerrard and the wholehearted Jamie Carragher, but Owen headed wide. The watching Tord Grip, Sven-Goran Eriksson's assistant, will have at least warmed to the sight of an all-English move.
Liverpool raised the tempo after the break, responding to the Kop's exhortations of "attack, attack, attack". Hamann, increasingly influential, almost scored but his flicked header from Gerrard's free-kick skimmed over.
Liverpool were in the mood and their heightened sense of urgency was soon rewarded. Baros's poacher's strike climaxed a lightning break, the move brimming with ambition at last catching out Marseilles' midfield and defence.
Owen accelerated the surge, slipping the ball through the middle for Gerrard to chase. The England midfielder collided with the advancing Barthez and the ball fell clear to Baros who poked it home under pressure, much to the Kop's delight.
Marseilles, though, began showing signs of a comeback inspired by their substitutes, Demetrius Ferreira and Camel Meriem.
It was Meriem who created the Marseilles equaliser, lifting the ball back in to the area for Drogba to escape from Hyypia and Stephane Henchoz and fire firmly past Kirkland.
Drogba almost registered his 23rd of the season moments later but Finnan and Kirkland combined to block his sight of goal. A caution for Barthez for some obvious time-wasting - and a near-chance for Hyypia cleared off the line - lifted Anfield's mood only temporarily.