Liverpool have lost their final game before Saturday's FA Cup final by going down to Fulham at Anfield.
Fulham were a goal up after just five minutes when an off-balance Martin Skrtel diverted a John Arne Riise cross into his own net.
Martin Jol's men almost doubled their lead minutes later but Russian forward Pavel Pogrebnyak was denied by Doni after being set up by Clint Dempsey.
Liverpool, who were without star duo Steven Gerrard and Luis Suarez because of Saturday's upcoming final against Chelsea, struggled to impose themselves in the opening period.
They came closest to an equaliser when Mark Schwarzer failed to hold a Jonjo Shelvey shot. With the ball squirming towards goal, Fulham centre-back Brede Hangeland managed to nick away from danger.
Hangeland was again on hand to prevent a goal early in the second half, with Maxi Rodriguez just about ready to pull the trigger the big Norwegian slid in to clear.
Moments later Fulham came within a whisker of going two ahead when substitute Kerim Frei clipped the post after dancing around a Liverpool challenge.
Dempsey then wasted a chance to make it 2-0 after being slipped through by Frei. The in-form American attempted to curl past Doni but the Brazilian read the effort and saved comfortably.
Dempsey had another chance to seal the win but he again couldn't beat Doni after Skrtel's headed backpass fell short.
Three points for Martin Jol's Cottagers sees them draw level on points with Liverpool in eighth place.
