The Republic of Ireland international lashed home a vicious 20-yard effort with just 11 minutes remaining to lift Fulham out of the relegation zone while ensuring David Moyes' side slumped to a third defeat in their opening four games of the campaign.
For much of the match such a result had seemed unlikely as Everton cruised into a first-half lead thanks to Tim Cahill's header and rarely looked troubled.
But a much-improved home side emerged for the second period and, after Paul Konchesky's deflected effort had got them back on terms, Duff smashed home the winner to send the Craven Cottage fans wild.
It was a surprise that the game ended with such incident and drama as for long periods both teams seemed short of inspiration, with the two goalkeepers going long spells without having anything to do.
In the case of Fulham's David Stockdale, that would have been a relief, however. The 23-year-old was a surprise replacement for Mark Schwarzer, who had failed to recover from a neck injury, and must have been bracing himself for a barrage of high balls from the visitors.
Yet they failed to arrive, although the one time a quality set-piece did come into the box, Cahill rose above Dickson Etuhu - who is four inches taller than the Australian - to plant a header into the corner, giving Stockdale no chance.
However, Fulham improved dramatically after half-time and were rewarded when Konchesky lashed home from 20 yards after Danny Murphy's free-kick had been blocked, although replays showed he was aided by a huge deflection off Sylvain Distin.
And after Everton were further disrupted by the loss of their captain, Phil Neville, who was carried off with a serious-looking injury, Fulham took complete command.
It fell to Duff to deliver the final blow to Moyes' side, though, cutting in from the right wing to arrow a shot across Tim Howard and into the far corner of the net to leave Everton second from bottom in the table with only pointless Portsmouth below them.