City, who had been seeking their third successive League win, produced an impressive display in the opening hour which must have impressed owner Thaksin Shinawatra on his return to Eastlands.
But in the final quarter of the game Fulham staged a remarkable recovery with two goals from substitute Diomansy Kamara and another from Danny Murphy as they came back from the dead to leave City's fans stunned.
And after failing to win away for over 18 months, Fulham have now recorded back-to-back away successes to give their survival hopes a massive shot in the arm.
Though City established a 2-0 lead it was by no means a commanding advantage. Three times in the opening half City were indebted to keeper Joe Hart who made super stops to deny Clint Dempsey, Jimmy Bullard and David Healy.
City made the breakthrough in the tenth minute with a classy goal as Martin Petrov's cheeky back-heel released Ireland who scored with a spectacular shot from the left edge of the penalty area.
And in the 21st minute City doubled their advantage when Darius Vassell cut the ball back from the right for Benjani to fire home his third goal for City with an effort he couldn't miss.
City ought to have stretched their lead early in the second half when Vassell and Benjani were both denied by keeper Kasey Keller while Benjani also headed over when completely free.
They looked like proving costly misses as Fulham staged a spirited comeback.
They finally got onto the score-sheet in the 59th minute when Kamara, who had only been on the field for five minutes, twisted and turned to beat Vedran Corluka and fire a shot through the legs of keeper Hart.
Three minutes later Fulham were desperately unlucky not to be on level terms when Bullard's free-kick was kept out by a brilliant save from Hart.
Fulham's renewed confidence was rewarded when they won a penalty 12 minutes from time after Sun Jihai had held down substitute Erik Nevland.
Danny Murphy's spot-kick was saved by Hart who watched in anguish as the ball rebounded to the midfield player to fire home from six yards.
In a thrilling finish both Fulham and City wasted a hatful of chances before the visitors snatched victory in the second minute of stoppage time.
Murphy released Kamara who raced into the penalty area to rifle a shot into the roof of the net to spark amazing celebrations both on and off the pitch.