The Portuguese striker zipped past Marcel Desailly before attacking the penalty area.
He cut back to get a better scoring position and did not disappoint the Fulham faithful as he unleashed a fabulous left footer that sailed past a helpless Carlo Cudicini and nestled into the far corner of his net.
It was no more than Fulham deserved as lacklustre Chelsea drop to fourth place, ahead of Liverpool on goal difference alone.
Chelsea had the best of the early chances - none more so than Jimmy Floyd Hasselbaink who failed to capitalise on a one-on-one with Maik Taylor the Fulham goalkeeper on nine minutes.
But the home side got their noses in front on 37 minutes and it owed much togood fortune.
A Gianfranco Zola free kick was misjudged by Taylor, the ball bounced onto the crossbar and John Terry directed the ball back towards goal off the upright, before a luckless Alain Goma directed the ball into the net.
Chelsea desperately needed a second goal and Frank Lampard missed the chance of the season after 56 minutes.
William Gallas got to the left byline before getting in his cross that Taylor failed to hold and the ball fell invitingly to Lampard who could only thrash the ball against the crossbar.
Fulham gained in confidence from this let off and Boa Morte's wonder strike was no more than they deserved.
A Zola ping from long range was goalbound but Taylor managed to tip the ball over the bar.
Substitute John Collins almost stole it for the visitors in injury time when his fine curling effort just skimmed the top of the net.
Chelsea substitute Eidur Gudjohnsen also could have spared coach Claudio Ranieri's blushes but his late, late left-footed half volley from the edge of the penalty area was inches wide of Fulham's left upright.