With the match poised delicately at 2-2 following Fulham's remarkable comeback from a 2-0 deficit, the Argentinian produced a moment of world-class magic to score the winner and keep the Blues well out in front in the Premiership title race.
Chelsea took full advantage of a breakdown in a move on 74 minutes and the ball fell to Joe Cole, wide on the left.
The England midfielder whipped down the line before sending over a deep, inch-perfect cross into the Fulham penalty area.
Crespo, quiet for most of the match, then found the perfect position on the angle of the six-yard box and met the cross with an exquisite left-footed volley.
The ball sailed across the despairing left-handed dive of substitute goalkeeper Tony Warner and into the far corner of the net.
It was a sign of confidence and spirit from the Premiership champions that they raised their game at the vital moment and won three more precious points.
Fulham, who have not won away from Craven Cottage in the league this season proved that energy and commitment can result in good performances and they dragged themselves back into the game when all looked lost.
After three minutes the Blues took the lead. Arjen Robben terrorised right-back Dean Leacock before seeing his fine cross cleared for a corner.
Up popped Frank Lampard who clipped in a corner which was met by Robert Huth's header. William Gallas ghosted into the far-post area and slotted home the ball with a cushioned right-foot volley past Mark Crossley.
The champions increased their lead on 24 minutes. This time it was a trademark Lampard shot from 25 yards out. It took a cruel deflection off the outstretched arms of Sylvain Legwinski, fooling Crossley in the process and into the net.
Chelsea goalkeeper Petr Cech, imperious in the Chelsea net then showed that he too is fallible.
Somehow, on 29 minutes, he managed to let slip a simple Luis Boa Morte free-kick through his legs. Brian McBride, back on the pitch following stitches in a cut eye, was first to pounce and scrapped the loose ball home from two yards out.
Fulham came out for the second half rejuvenated while Chelsea brought on Eidur Gudjohnsen for a lacklustre Shaun Wright-Phillips.
Gudjohnsen could have scored with his first touch, a vicious right-footer from the edge of the area, but Crossley parried the ball clear.
Then, on 50 minutes, Zat Knight handled the ball in the area but referee Graham Poll adjudged the ball had already gone out of play for a corner. TV suggested otherwise.
Five minutes later and Fulham were level. Sloppy defending saw McBride upended by Cole in the Chelsea area and Heidar Helguson confidently tucked away the spot-kick.
Fulham could count themselves unlucky not to have given a second penalty on 80 minutes. John Terry clearly handling a Boa Morte piledriver, but such is the luck of champions who ran out 3-2 winners.