Liverpool did not have Steven Gerrard around to save them this time after a limp performance, his torn groin muscle having a damaging impact on Rafael Benitez's side.
Fulham, with one of the best defensive records in the top flight, have never won at Anfield and rarely looked like doing so this time.
But their dogged performance claimed only their second away point of the season and also secured their third goalless draw in eight visits to Anfield.
At least they had worked out how to contain a Liverpool side who lacked ideas and inspiration. Not even the return of Fernando Torres to the starting line-up helped much.
Defenders Aaron Hughes and Brede Hangeland had a firm grip on Robbie Keane and Torres for most of the game, and Liverpool could not find a way through.
Torres returned to the Liverpool starting line-up for the first time since the October 5 win at Manchester City. Two appearances as a substitute at Bolton, and for Spain against Chile in midweek, confirmed his recovery from a hamstring problem.
Boss Benitez rested Xabi Alonso on the bench and brought in Alvaro Arbeloa, Lucas and Torres from the side that started the win at Bolton last weekend.
Fulham, who arrived having suffered just two league defeats in seven and won three of the last four, retained the side that beat Tottenham last weekend.
But with Gerrard out it was maybe a surprise that Benitez opted to also rest Alonso, who has been in outstanding form this season. It meant he had two holding players, Lucas and Javier Mascherano, in central midfield and a lack of creativity.
Liverpool still started at pace, but the opening exchanges produced just one decent chance. Fabio Aurelio's 40-yard cross-field pass picked out Arbeloa, and his lay back was side-footed just wide by Dirk Kuyt after four minutes.
Fulham were confident and organised, with Jimmy Bullard and Danny Murphy having plenty of the ball.
The danger signs were there when a hook from Andrew Johnson, the ex-Everton man getting a warm welcome from the Kop, forced Jose Reina into a scruffy save.
Fulham had threatened from set-plays and the movement of Bobby Zamora, before Liverpool produced the best chance of the half.
Aurelio's ball in from the left looked to deflect off Torres and Bullard before falling for Keane after 29 minutes. But Mark Schwarzer was out bravely to get his body in the way of the Irishman's eight-yard shot.
Then it was Reina that kept Liverpool level. Referee Mark Halsey played excellent advantage after 34 minutes when Aurelio clattered into Clint Dempsey.
Zamora raced away down the right, reached the line, before laying the ball back for Bullard to fire in a fine effort from the edge of the box that the Spanish keeper turned away at full stretch.
Torres had a header that went wide and a low drive from Kuyt's pass that Schwarzer held, to underline miss-firing Liverpool's problems.
Liverpool were much sharper after the break and when Keane's pass found Torres, the Spaniard curled a fine shot just over the far angle.
Then after 50 minutes Torres surged past John Pantsil to lash in a angled effort that Schwarzer palmed away.
The crowd had been calling for Alonso's introduction from the half-hour mark, and as Liverpool's drive slowed and frustration crept in, the midfielder's name boomed down from the Kop.
Benitez answered the chorus after 64 minutes, taking off Mascherano and sending on Alonso.
After 69 minutes Albert Riera's cross was met on the full by Kuyt, but Schwarzer made a fine save to his left.
Liverpool then sent on Ryan Babel in place of Riera after 78 minutes, with Nabil El Zhar taking over from Kuyt four minutes later. Fulham sent on Zoltan Gera for Dempsey after 84 minutes.
The Reds were looking ragged now, bereft of ideas, and even Alonso fired high over after being set-up by Babel.
Lucas saw a 20-yarder blocked by Pantsil and Daniel Agger saw a header clear the bar.