HEREFORD United gained their third League One scalp in this season's competition as they moved into the FA Cup fourth round for the first time in 16 years.
Simon Johnson's fine strike settled the issue in the 71st minute in a game which Tranmere dominated for long periods.
Rovers began the match at a furious pace and drove Hereford back for the first 10 minutes. In the first minute, a fine run by Jennison Myrie-Williams ended in a cross which Gareth Taylor fired wide.
Then Myrie-Williams raced on to a short free-kick and sent another fierce drive wide.
Hereford, at this stage, were finding it hard to break out of their own half but, in the 17th minute, Robbie Stockdale did well to clear a dangerous Trent McClenahan cross.
It then took a good save by Wayne Brown, who came out bravely to block at the feet of Calvin Zola, to keep the scoresheet blank.
At the other end, Danny Coyne came out of his area to hack clear as Robinson raced on to a Kris Taylor pass.
But Brown was soon back in the action, stooping to hold a 20-yarder from the dangerous Myrie-Williams.
Hereford almost took the lead at the start of the second-half when Robinson forced a fine save from Coyne with a header from McClenahan's cross.
But Tranmere fought back strongly and Hereford had to defend superbly to keep then at bay. The Bulls were assisted by some wayward Rovers finishing with Zola often the culprit.
The big striker sent a shot and then a header wide from good positions. But his luck was out in the 68th minute when he made space cleverly only to lash a shot against the bar.
Three minutes later, Hereford took the lead with a superb individual goal from Johnson who made ground before driving a low shot into the corner of the net from 20 yards.
Hereford almost extended their lead in the 79th minute when Trevor Benjamin's header from McClenahan's cross came out off a post.
But Brown came to Hereford's rescue two minutes later with a fine save from Zola's low drive.
The hosts controlled play in the closing stages to earn their fourth round tie with local rivals Cardiff City.
Hereford: Brown; McClenahan, Beckwith, Collins, Rose; Johnson, Smith, Diagouraga, Taylor; Benjamin, Robinson. Subs not used: Ingham, Broadhurst, McCombe, Palmer, Gwynne.
Attendance: 6,471.
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