Sunderland dominated the first half and created numerous chances, with Kieran Richardson squandering the best opportunity when blasting well over from 12 yards.
But Bolton came out a different side in the second period and Riga Mustapha blasted over before Jussi Jaaskelainen had to be alert to clear a Djibril Cisse cross at the other end.
Gary Cahill could then have won it at the death but his header was kept out by a fantastic Marton Fulop diving save.
The draw see's Gary Megson's side reach the magic 40 points mark but Sunderland are still not safe with 36 points.
The Black Cats have a five-point advantage over Newcastle and Middlesbrough, who meet at St James' Park on Monday, as well as West Brom.
In his programme notes, Megson had stressed Bolton were still not safe but that message did not get through to his team as the Trotters were sterile in the opening half, failing to muster one decent shot at the Sunderland goal.
BoosIt was a performance which did not meet with their supporters' approval, with boos heard at regular intervals long before the half-time interval had been reached.
For Sunderland, it should have been manna from heaven, a perfect opportunity to collect the three points required to virtually ensure their own safety after a tortuous campaign.
But the Black Cats are bereft of confidence just now and presented with a wide open door, they still struggled badly to walk through it.
Teed up by Kenwyne Jones, Richardson had an early chance to settle a few Sunderland nerves but his shot sailed over and it was to become a familiar story of a one-sided first-half.
Dean Whitehead's overhead kick, another Richardson effort and a low drive from the industrious Grant Leadbitter all threatened the home goal without looking like breaching it.
If Jones had managed to get himself on the end of something, it might have been a different story.
But the best the forward could manage was a couple of assists, and an anguished flailing of the arms as Richardson ignored him - even though he was unmarked and in a central position - and got robbed by Gavin McCann after Andy O'Brien had gifted him possession.
Second-halfFaced with the mutinous reaction of his own disgruntled supporters, Megson decided to act, introducing Mark Davies for a totally ineffective Tamir Cohen.
A £1million arrival from Wolves in the January transfer window, Davies managed to instil a sense of urgency among his team-mates which had been so badly lacking before.
The youngster drove one bullet strike straight at Calum Davenport, with namesake Kevin also responding to Davies' promptings, causing momentary panic in the Sunderland box with a neat flick-on which eventually ran through to Fulop.
It meant Sunderland were not dominating as they had done before, even if they were still carving out opportunities for themselves, including Richardson's long range free-kick which went over.
Jones then limped off to be replaced by Cisse, whose arrival met with the approval of his side's support, even if Richardson was the player who continued to hog the chances, a half-volley bobbling wide despite being on his better left-foot.
Jaaskelainen stuck out a boot to hack a Cisse cross-shot away from danger before Bolton made one last concerted attempt at breaking the deadlock.
Mark Davies rushed his shot when namesake Kevin flicked a header into his path, then fellow substitute Riga drove a volley into the ground when he should have done much better.
The real drama was still to come though, with Fulop emerging the hero to deny Cahill as Sunderland inch nearer to safety.