Having taken just eight points from as many capital clashes prior to this contest, another night of frustration appeared to be in store until Mikael Forssell emerged from the bench to turn in a late winner.
Claudio Ranieri's side, who began the evening 11 points adrift of fourth place and that lucrative spot in Europe's premier club competition, were twice pegged back by goals from Louis Saha.
But Forssell ensured a new beginning for a late season bid for the top four on a newly-laid Stamford Bridge surface.
Captain Marcel Desailly, back after missing the 2-1 defeat at Charlton with a hamstring, should have returned with an immediate impact.
But when he unexpectedly arrived on the edge of the six-yard box to meet Graeme Le Saux's low centre, after Eidur Gudjohnsen's dummy offered the opportunity, he stabbed wide.
It would have been a perfect start for Chelsea, who began the night 11 points adrift of a Champions League place.
But they might have been behind to their less illustrious neighbours in the sixth minute after Desailly conceded a corner.
From Steed Malbranque's delivery from the right, Steve Marlet rose highest to head powerfully against the crossbar and the hosts cleared.
At the other end, Jimmy-Floyd Hasselbaink twice went close to adding to his 18 Premiership goals for the season.
First, he hit the side-netting from Mario Melchiot's through ball.
Then, it took a perfectly-timed sliding tackle from Alain Goma to divert a goal-bound drive.
But Chelsea did score with their next attack of note from an unlikely source.
Melchiot ran unchallenged from right-back once again before cutting in to shoot past a static Edwin van der Sar with his left foot, via a deflection off Rufus Brevett.
Yet, within 60 seconds of Chelsea's opener, Fulham were given the chance to level in controversial circumstances.
A burst into the area by Louis Saha was halted by a well-timed tackle by William Gallas - but referee Peter Jones pointed to the spot as Saha hit the turf.
Saha, last season's top scorer in English football, took the kick himself, tucking the ball inside Carlo Cudicini's right-hand post with the goalkeeper diving left.
Chelsea were incensed by the decision and had a right to be so.
Their retribution was telling with Zola testing van der Sar with a right-foot curler before another effort from the diminutive Italian was superbly repelled by the Holland international at the expense of a corner.
Then, just short of the half-hour, Chelsea regained the lead.
Le Saux exploited holes in a Fulham defence that had conceded eight goals in three consecutive defeats by inviting Eidur Gudjohnsen to run deep into the visitors' territory.
The Icelandic striker picked his spot and sidefooted past van der Sar for his 12th league goal and 19th in all this season.
After Malbranque watched a volley deflect behind of Gallas, Fulham were denied a second, this time seemingly legitimate, penalty as Marlet was tripped by Frank Lampard's trailing leg.
In fact, it was only woeful finishing from last season's Division One champions that prevented them going in level at the break.
Abdeslam Ouaddou inexplicably directed his free header from a Malbranque corner wide.
And Saha, seizing on an inventive ball from strike partner Marlet, galloped clear before dragging wide on the stroke of half-time.
The home side were always a threat with Zola lurking in the void behind Hasselbaink and Gudjohnsen.
Three minutes into the second period, Hasselbaink found Zola's feet, allowing the Italian to turn and send a shot that lacked power into van der Sar's grasp.
In contrast to the first half, chances were scarce after the interval.
Emmanuel Petit, who hobbled off the field moments later, volleyed straight at van der Sar as a cross was cleared to the edge of the area.
And Cudicini touched round the post as Saha tried his luck from the right-side of the area.
Coaxed forward by John Collins, however, Fulham hauled themselves level again with 17 minutes left.
Collins sought out Marlet's pace down the left and the France international forward checked his run and picked out Saha, who beat a bizarre bicycle kick from Gallas to head in his second of the night.
Ranieri responded immediately by employing his third and final substitute, Forssell, in place of Gudjohnsen.
And Forssell continued his phenomenal record coming from the bench with his seventh goal from such a position in 12 games.
Fellow replacement Jesper Gronkjaer lifted into the box and Forssell controlled on his chest and swept home with his right foot eight minutes from time.