Neither side could complain with the outcome, though Fulham will be frustrated that a series of second-half chances were foiled by some resolute defending.
At one point in the second half Sunderland had a four-on-one overlap and a goal appeared certain, but an abysmal pass from Darren Bent ruined the moment.
It was a dismal spectacle that improved a little in a second half controlled by Fulham, with Clint Dempsey the focal point of their attack.
Resonding to reported interest from Liverpool and Wolfsburg, manager Mark Hughes stated on Friday that Dempsey would not be sold in the transfer window next month and the USA attacking midfielder showed why the Welshman is determined to keep him, proving a constant thorn in Sunderland's side.
Fulham barely mustered an alternative threat, however, and are struggling in the final third with Bobby Zamora and Moussa Dembele injured.
Hovering above the relegation zone, they looked short on confidence and desperately need a win to kickstart their climb up the table.
The match started at a brisk pace with a swinging arm from Lee Cattermole on John Pantsil provoking a furious response from home fans.
Dempsey tested Simon Mignolet with a goalbound looping volley before defender Anton Ferdinand limped off in the 10th minute, replaced by Ahmed Elmohamady.
Nedum Onuoha headed a corner over from an awkward angle but it was only a half chance.
Fulham were suffering from conceding possession far too easily in the final third, though both sides were struggling to build any rhythm amid a frantic opening 20 minutes.
The home defence dealt with a dangerous ball by Jordan Henderson, crowding out Bent and Danny Welbeck.
Fulham finally burst into life in the 27th minute when Zoltan Gera sent Diomansy Kamara into space only for the Senegal striker's final ball to be cleared by John Mensah.
Brede Hangeland produced a timely block on a cross, but the free ball sparked a penalty area scramble that was eventually cleared to safety.
The half was short on quality but Sunderland attacked with more conviction, Phil Bardsley setting up a half-chance for Bent who failed to keep his header on target after leaping high to outjump Hangeland.
Pantsil then got his body in the way to block an attempt by Bent, who on this occasion was teed up by Henderson.
Andrew Johnson replaced Kamara for the second half, an admission by manager Mark Hughes that Fulham desperately needed some inspiration.
But the Cottagers' next raid came not through Johnson but Dempsey, whose chip towards the top right corner was plucked from the air by Mignolet.
Fulham were attacking the second half with far greater vigor and they nearly crept ahead in the 56th minute, but Dempsey just failed to reach Carlos Salcido's brilliant cross.
It then took a cleared header from Bardsley, the last line of defence, to prevent the home side from taking the lead through Dickson Etuhu's goalbound effort.
All of Fulham's best moments were being provided by Dempsey, who saw another delicate shot stopped by the arm of Onuoha just outside the area.
Mignolet produced an excellent save after Johnson had pulled the trigger from point-blank range, but the Cottagers were almost hit on the break.
Sunderland rushed upfield with only Pantsil defending against four players but Bent's crucial ball to Asamoah Gyan was terrible.
Johnson teed up Dempsey but this time Cattermole made the crucial block.
Kieran Richardson then tugged on Dempsey's shirt to concede a free kick on the edge of the area, but Gera's delivery was tame.
Bolo Zenden sent a low drive narrowly wide of the right post from 30 yards and was then felled by a clearance from Pantsil before groggily rising to his feet.
Bent was flagged offside after being put one on one with Mark Schwarzer, but he missed anyway, summing up a poor match.