Both sides have struggled in the opening weeks of the campaign, but a point apiece at full time was a fair enough result in West Yorkshire.
The Blades had the better chances in frantic opening 45 minutes with John Lundstrum and Enda Stevens both testing Alphonse Areola from distance.
But it was Scottish international Oli McBurnie that missed their best early chance as Areola reacted brilliantly to bat away his header.
That slice of luck allowed Fulham to gain the ascendency after the break and the Cottagers were gifted a perfect chance to edge in front on the hour.
Jack Robinson was penalised for handball inside the box but the normally reliable Aleksandar Mitrovic fired his spot kick off the bar.
But despite their rock bottom confidence, Fulham were not to be denied an opener, as Ademola Lookman smashed home with 12 minutes left.
The visitors looked to batten down the hatches in the final minutes but United found themselves a late equaliser as veteran Billy Sharp tucked home from the spot.
FULL TIME AT BRAMALL LANE IT’S SHEFFIELD UNITED 1 FULHAM 1