Ibrahim Olutade cut in from the left and crossed the ball into the box where it deflected off Blues’ Ryan Henshaw and looped in over keeper Athur Janata’s head.
New signings Jerry Amoo and George Craddock were both on the bench for Jamie Cureton’s side, but the visitors were without the influential Ryan Charles and striker Luke Callander and suffered a further blow shortly before half-time when Cureton limped out of the action,
Chris Gregan caused the Tanners problems with his long throw while Curton set up Johnville Renee but he couldn’t meet the cross.
Janata did well to keep Blues on level terms with a superb save from Olutade, and also twice denied Skinner.
Ben Worman was unlucky not to net his fourth goal since joining from Cambridge United when he met Mark Haines’ corner, but his effort was deflected wide.
Within a minute of what proved to be the game’s only goal Cureton left the action to be replaced by Amoo, and Blues did little to get back into the game before the break.
Henshaw was twice desperately unlucky not to level, but at the other end Haines was forced to make a last ditch clearance to deny the impressive Olutade.
Blues finished strongly, with Nathan Livings hitting a post and firing the rebound wide from six yards, and substitute Alfie Mason should have done better when given room, but the Tanners held on for all three points as the visitors dropped a place to 11th.
BISHOP’S STORTFORD: A Janata, B Sampayo, C Gregan, S Robbins, R Henshaw, M Haines (G Craddock 67), J Renee, N Livings, J Cureton (J Amoo 36), O Miles (A Mason 71), B Worman; Unused subs A Warman & H Belaid
LEATHERHEAD: Oualah Driver Krasniqi Hester-Cook Salmon Nnamani Skinner Gallagher Okojie Olutade Gregory; Subs: Dadey Sardinha Wallace Ikebuasi McGee