It was the home side that should have opened the scoring inside the first five minutes when a clever ball from the outside of Fabio Aurelio's boot found Dirk Kuyt behind the Fulham back line but, after bringing the ball down, the Dutch winger lacked the composure to hit the target and dragged his shot wide.
With no Steven Gerrard in the side and Lucas Leiva partnering Javier Mascherano in the middle of the park, Liverpool lacked any creativity and it was the Fulham duo of Danny Murphy and Jimmy Bullard who looked to have the more quality around the centre circle.
A scrappy first 20 minutes suited Fulham and they should have done better from a trio of volleyed passes starting with Murphy to Simon Davies then on to Jimmy Bullard whose overhead ball dropped over the shoulder of Andy Johnson.
The striker scuffed his shot straight at Pepe Reina in the Reds goal, much to the pleasure of the home crowd.
Kop favourite Fernando Torres looked to have found his match fitness again and a jinking run at two Fulham defenders on 23 minutes looked to have created a good shooting chance on the edge of the box but a last-gasp tackle by John Paintsil prevented the Spaniard from pulling the trigger.
Liverpool had the Cottagers pinned back in their own half for most of the game but, despite creating a hatful of chances, they never looked like breaking the deadlock.
The best chance of the game fell to Robbie Keane just before the half-hour mark when a low driven ball into the box flicked off an unsuspecting Leiva and fell into the path of the former Spurs striker who was one-on-one with Mark Schwarzer.
Despite claims for offside, Keane still took a shot but his panic-looking effort was blasted straight at the keeper who spread himself well and ended up saving the ball with his face.
Fulham managed to get a rare scoring chance five minutes later when a powerful run from Bobby Zamora took him past three players before cutting the ball back to Bullard who unleashed a 20-yard effort but Reina was alert enough to push the ball over his bar.
With a very organised back-line Roy Hodgson's men stood strong to whatever Liverpool threw at them and Schwarzer was forced to save a low drive from Torres just before the break.
After the restart it was Liverpool again who created the first chance when a curling right-footed effort from Torres sailed just over the top corner.
With no-one else in the team seeming able to have a strike on goal it was the Spanish striker who tested Schwarzer again on 51 minutes after his pace out stripped both Paintsil and Murphy, but his effort was blasted straight at the shot-stopper who palmed away the danger.
Having been calling for Xabi Alonso to be brought on since midway through the first half, Benitez seemed to be giving the fans what they wanted but the home crowd's cheers were soon replaced with groans of despair when he took off Mascherano instead of the expected Leiva.
With 20 minutes to go Liverpool started throwing everything they had at the wall of white in front of them and Kuyt was the next to hold his head in his hands.
A driven shot from Albert Riera against the legs of Paintsil flew to Kuyt whose first-time effort was heading for the top corner before Schwarzer appeared to pluck the ball out of the air.
With speculative efforts from Keane, Leiva and Daniel Agger in the closing stages Liverpool should have had the game well and truly wrapped up but Fulham stood strong and thoroughly deserved a point.