Leadbitter deftly swept home from the spot late on but victory was only assured after Jermaine Beckford missed a late penalty for Bolton.
There was a very cagey start as both sides took a very cautious approach, with the premium on possession and only rare probes forward.
Boro carved out the first real chance on 18 minutes as a poor punch by Bolton keeper Andy Lonergan from an Albert Adomah cross landed nicely for lapping full-back George Friend on the left of the box but his low 20 yard drifted wide of the post.
Then on 39 minutes Boro won a corner and when Leadbitter's ball curled to the far post, defender Ben Gibson climbed highest but his header flashed wide.
Then in stoppage time Boro threatened as Mustapha Carayol collected a cross and laid it back for Jacob Butterfield whose shot struck a defender hit Alex Batiste on the hand from close range, leaving fans screaming for a penalty but the referee waved play on.
Bolton started brightly after the break and almost struck out of the blue on 50 minutes as Leadbitter played a dangerous back-pass that sent Beckford racing into the box but on-loan Shay Given just beat him to it to clear.
Then on 53 minutes they pressed again as Jay Spearing slipped a ball into the box for Beckford but his first time angled effort flew well wide of the far post.
And on 56 minutes Bolton went close again as Kevin McNaughton chipped over the defence for Beckford to beat the offside flag but his 20 yard volley screamed over.
Bolton had a strong call for a penalty on 64 minutes as Rhys Williams barged into Beckford as the pair challenged for a cross to the far post but appeals were waved away.
Boro went close on 70 minutes as substitute striker Curtis Main cut in from the right to flash a low 20 yard effort just wide of the far post.
The home side won a penalty on 82 minutes as Marvin Emnes was hauled down as he tried to control a Williams cross and Leadbitter calmly slotted home.
Bolton could have levelled as they won a penalty of their own on 88 minutes as Williams brought down Andre Moritz on the right of the box but Beckford blazed high over the bar.