Chasing a sixth successive win in all competitions, Leeds had Robinson and Jonny Howson in place of Andrew Hughes and Neil Kilkenny, who started the last league game against Carlisle.
Hereford, without an away point this season, gave a debut to central defender Bruno N'Gotty, on loan from Leicester and he organised the back four superbly as Leeds failed to make their overwhelming first-half possession count.
Hereford, showing little ambition, left former Everton and Plymouth striker Nick Chadwick alone up front whenever Leeds had the ball, which was often.
Although Robinson and Jermaine Beckford struggled with their passing, teenagers Fabian Delph and Aidan White showed their immense potential and when Delph fed White he ghosted past two defenders before seeing his shot deflected just past the post for a corner.
Robinson wasn't far wide with a 30-yard drive and a superb through ball from Delph bounced awkwardly for Beckford who was about to strike from 18 yards.
Hereford were restricted in the first half to a couple of hopeful shots from Stephen O'Leary who was booked after only 14 minutes for clattering into Howson.
Leeds created two chances just before the break but desperate defending kept out Jonathan Douglas and Luciano Becchio.
Beckford went close with a header and a shot just after the interval and it needed a two fine saves by Randolph to prevent Hereford falling behind.
However, they finally cracked in the 72nd minute when Beckford's cross saw Randolph parry Becchio's header only for Robinson to head the rebound home from ten yards.
Hereford created two late chances, but Matt Done and substitute Moses Ashikodi squandered them.