Kevin Davies had given Bolton a 47th minute lead after they had the lions share of the play, although Sunderland had chances to at least grab a share of the points.
Nolan had Bolton's first chance of the game and was unlucky with a curling shot in the 17th minute.
The midfielder missed the target though and at the other end Kevin Kyle saw a left-foot volley fly over the bar from close range.
Bolton pressed and in the 19th minute full-back Ricardo Gardner forced a fine save out of Sunderland shot-stopper Kelvin Davis.
The defender's left-foot strike looked to be flying into the far corner, but Davis did well to deny him.
Bolton were on top and as their momentum told, Ricardo Vaz Te saw a right-foot shot go wide in the 27th minute and then two minutes later he volleyed over the bar when he should have scored.
On the stroke of the half-hour mark the impressive Gardner limped off with an injury and was replaced by Henrik Pedersen, but that didn't stop Bolton's progress.
Midfielder Jay-Jay Okocha fired wide from 25 yards in the 33rd minute with a rasping right-foot drive, before Nolan had a point-blank shot saved by Davis five minutes before the interval.
In the 41st minute Okocha fired wide of the left-hand post and then two minutes later saw a 30-yard right-foot drive fly wide of the target.
But whatever Bolton could do, they just couldn't hit the back of the net.
Allardyce's men were nearly made to pay on the stroke of half-time when Grant Leadbitter saw a volley blocked on the line by Frenchman Bruno N'Gotty.
Allardyce must have had stern words for his team at half-time as two minutes after the resumption Greece international Stelios Giannakopoulos crossed for Davies, who made no mistake heading home at the near post.
Sunderland would have levelled but for a wonder-save from Bolton keeper Jussi Jaaskelainen.
Tommy Miller fired a firecracker of a shot on target in the 49th minute, but Jaaskelainen produced a brilliant finger-tip save to push the ball round the post.
Both sides continued to battle and in the 60th minute Okocha crossed for Gary Speed, but he should have done better from close range, heading wide of the target.
Bolton were by far the better team by now and in the 85th minute they duly got their second goal, deserved for sheer perseverance.
Goalscorer Davies crossed, Mexican hitman Jared Borgetti forced Davis into a point-blank save, but Nolan was on hand to grab the scraps. His viscous volley left the keeper no chance after his initial excellent block.
Miller nearly gave Sunderland some respectability in the 86th minute, but his miss summed up a miserable day for the North East visitors.