Fulham ended its run of four defeats by clinging on for a point at Craven Cottage - but was let off the hook by referee Keith Stroud's decision to disallow a stunning 52nd-minute free-kick by Kieran Richardson - and the woodwork.
Richardson had already suffered when his 41st-minute free-kick saw the ball hit both posts, then struck the woodwork again via Cottagers goalkeeper Mark Schwarzer, who eventually gratefully grabbed it.
So it looked like justice was done 11 minutes after the break when he arrowed his set-piece into the top corner - only for referee Stroud to rule it out for interference by Pascal Chimbonda in the Fulham wall.
Television replays appear to show that Chimbonda actually tugged the arm of team-mate, Dean Whitehead.
A point was just about what Fulham deserved though. It made as many chances as its visitors and if Zoltan Gera could have aimed straight it might have earned a valuable win.
Although Sunderland passed more sharply and struck the woodwork in four separate incidents, Fulham never lacked for effort and made some of the better opportunities.
Sadly, most of them fell to the feet of Gera, who had already scored twice for it this season since his summer move from West Brom.
However, in the ninth minute he steered a shot from 10 yards straight to Chimbonda - standing on the Sunderland line with goalkeeper Craig Gordon grounded.
And seven minutes later he failed to connect altogether with Andrew Johnson's perfect low cross from even closer range.
Later the Hungarian failed to beat Gordon with two close-range headers, before he was substituted 17 minutes from time.
Chimbonda was in the right place again in the 37th minute when he heroically headed Bullard's fierce, rising shot over his own crossbar.
Earlier, Schwarzer had to save sharply from Djibril Cisse and Richardson - but was left thanking his lucky stars courtesy of Richardson's woodwork woe.
It certainly did not look like it was Richardson's day when he stepped up for another free-kick nine minutes after half-time, crashing it past Schwarzer only for Stroud to harshly rule the effort out.
Fulham had tried to crank up the pressure towards the half-time break and after its amazing escape the luckless Gera had another near-miss at the other end when his diving header was well saved by Gordon.
Fulham had plenty of possession, thanks mainly to the energy and determination of captain Danny Murphy and the ubiquitous Bullard.
However, strikers Bobby Zamora and Johnson - returning from suspension - were well policed by Anton Ferdinand and Danny Collins.
Johnson had scored in each of his previous five appearances against Sunderland but rarely got a look in this time.
Frenchman Steed Malbranque wanted to make an impression against his former club but only earned a booking for an over-zealous challenge on John Pantsil - much to the joy of the home crowd, which jeered him all afternoon.
Sunderland's start to the second half promised a breakthrough and Aaron Hughes had to head off Fulham's line when Schwarzer's weak punch fell at Richardson's feet for him to execute a neat lob.
Richardson was denied again with his disallowed free-kick, while Sunderland struck the woodwork again when Cisse's fierce shot was too much for Schwarzer but came back off the bar.
Fulham was clinging on at times but still managed top raise some scares in the Sunderland penalty area, notably when Zamora and Bullard brought saves from Gordon.
However, Sunderland substitute Andy Reid would have been clean through on the home goal in the closing stages as he chased a Malbranque pass - but for Cisse straying offside.