Former Black Cat El-Hadji Diouf clambered off the bench to salvage a 2-2 draw for Blackburn at Ewood Park - but the home side were a fingertip away from claiming all three points.
Darren Bent's second half double looked likely to earn Steve Bruce's men a rare win but Rovers clawed back first through Morten Gamst Pedersen then Diouf.
Then in a grandstand finish which bore little resemblance to the dismal fare on offer in the first period, Marton Fulop brilliantly parried a point-blank header from Nikola Kalinic - before Chris Samba poked the rebound wide.
The bare statistics will point to Rovers extending their winless run to eight games, while Bruce's injury-hit Sunderland can now number just one win from 11.
Neither side had showed any sign of improving their winless recent records in a dismal first half, memorable only for the solid debut of David Meyler.
Meyler cut a composed figure in the centre of the visitors' midfield but all around him there were far too many nerves to fashion clear-cut chances.
An unusually careless back-header by Ryan Nelsen almost let in Bent in the 18th minute but the striker was pushed wide and the move came to nothing.
And two minutes later Rovers came close when Morten Gamst Pedersen curled over a ball to the far post and found Benni McCarthy, whose header from a tight angle found the roof of the net.
Meyler had the chance to make an instant name for himself when he let fly in the 22nd minute with a long-range strike which coasted wide of target.
Rovers, more desperate for a win in the circumstances, began the second period with a higher tempo but their anxiety to get forward played into the visitors' hands.
Against the run of play, Daryl Murphy threaded his way into the Rovers box in the 52nd minute and sparked the goalmouth melee which brought the visitors' opener.
Murphy's low cross was flapped by Robinson into the path of Jordan Henderson. When his shot was blocked by Ryan Nelsen, Bent was on hand to lash in the rebound.
But Rovers responded by drawing level inside a minute, McCarthy's flick leaving Pedersen in space down the left to cut in and drill a low shot in off the post past Marton Fulop.
Rovers maintained their new-found momentum and could have gone ahead in the 57th minute when Andrews just failed to connect with Pedersen's deep cross in front of goal.
But the visitors regained the lead against the run of play in the 65th minute when Henderson's punt forward sent Bent clear to slide a cool finish across Robinson and into the net for his 13th goal of the Barclays Premier League campaign.
Two minutes later Rovers came close to a second quickfire equaliser, as Pedersen crossed to the edge of the box where Nzonzi spooned a fine chance over the bar.
After Bent was played through again to fire a hat-trick chance inches wide in the 72nd minute, Allardyce had seen enough and responded with a triple substitution.
Forced to throw caution to the wind, the Rovers boss introduced Diouf, Franco di Santo and Nikola Kalinic in place of McCarthy, Jason Roberts and David Hoilett.
And in the 77th minute Allardyce's brave move paid off when Diouf got on the end of a cross by former Sunderland team-mate Pascal Chimbonda to head home the equaliser.
Rovers should have snatched victory in the dying seconds when Kalinic's header from a Pedersen free-kick was brilliantly saved by Robinson, with Samba failing dismally to convert the rebound.
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