A free kick from right on the edge of the area, in a central position on 63 minutes after Ben Futcher was bundled over by a Mangotsfield defender saw Celtic through tonight.
Peacock lifted the ball over the wall and into the right hand corner of the goal after striking the underside of the bar.
Until then it had been an fairly evenly matched contest, with Celtic slightly edging it.
Pickford hit the post early in the first half and Ayorinde should have done better but volleyed way over from 8 yards out. Courtney had a couple of chances, including a one on one with the keeper which Dyson in the Mangotsfield goal just scooped the ball from under his nose.
At the other end Mangotsfield hit the post after a rasping drive from Seal.
As the half progressed Celtic looked uneasy as Mangotsfield pushed up and started to take over the midfield.
Surprisingly even the home side seemed unable to get used to the pitch which has a pronounced slope running across with each corner seeming to fall away as well - as a result many balls ran into touch.
In the second half Celtic started as they did the first forcing Mangotsfield onto the back foot. On 58 minutes Ayorinde should have scored with a powerful header from 6 yards which was just wide.
Following Peacock's goal Mangotsfield pushed forward and were always liable to being caught on the break. Turley (on for Courtney) came closest to making it two when, with the keeper stranded well off his line, he curled a shot from 20 yards which was just outside the post.
Some resolute Celtic defending from Beesley, Murphy, Futcher and Co. in the final 10 minutes, with Fish's goal never really threatened, ensured Celtic travel to Gravesend