But the visitors will be ruing the one that got away as Jason Roberts passed up a gift-wrapped opportunity to seal victory.
A long clearance in the dying minutes of the game fell invitingly at the forward's feet. He did well to round Sunderland keeper Marton Fulop, but with the Sunderland goal at his mercy he somehow managed to slide his shot the wrong side of the post.
It was miss of criminal proportions and Roberts looked on in disbelief at his error.
Had he netted it would have been harsh on the hosts and buoyed by their lucky escape they pushed on looking for a last-gasp winner.
However, as for much of the encounter, they failed to find that killer pass in the final third. It was the same story for the red and whites in the opening 45 minutes.
The hosts had edged the first half in terms of both possession and attacks on goal, but having scored eight goals in their two previous league games, they were lacking a cutting-edge this time around.
Blackburn, on the other hand, put themselves about and got men behind the ball to restrict the Black Cats to half-chances.
In truth that was all they did in the opening half and they failed to offer anything in terms of attack.
Right-back Phil Bardsley went closest for the Wearsiders on 22 minutes, the ball reached him 22 yards out from goal and the defender cut on to his favoured left foot, letting fly with a shot that drifted just wide.
Seven minutes earlier, Steed Malbranque had a good chance to put Sunderland in front as the ball dropped to him on the edge of the 18-yard area. However, the Frenchman lofted his effort over the bar and into the stands when he really should have hit the target.
After the break Rovers were far more of an attacking threat and took the game to the hosts in the opening minutes of the second period.
The visitors even managed to find the net on 48 minutes, but it was ruled out as Chris Samba had used his hand to guide the ball goalwards and was booked for his troubles.
Morten Gamst Pedersen brought the save of the game out of Fulop on 53 minutes. The Rovers wide man curled in a free-kick from the edge of the box but Fulop, at full-stretch, managed to clear the ball on to the post and the danger was cleared.
The Sunderland keeper was again called into action on the hour mark as Keith Andrews raced into the area, he looked set to score, but the Hungary international got down well to block the ball out for a corner.
The hosts weren't without chances of their own in the second half, but by and large these were long-range efforts which never really troubled Paul Robinson in the visitors goal.
In the end, it was the Wearsiders who were happiest with the point gained, especially as Roberts let them off the hook so very late on.