But on the debit side the Merseysiders had defender Ian Goodison sent off in the 73rd minute. He was shown a direct red card for a two-footed challenge on Matt Done.
It took Rovers just eight minutes to open their account although they should have been ahead two minutes previously.
A mistake by keeper Peter Gulacsi set up Antony Kay, but his close-range shot was deflected for a corner.
But a goal was not long coming. Ian Moore chipped the Hereford defence and Bas Savage strode in to put a low shot past the keeper.
United could not get in a real blow at the home goal. At the other end Andy Taylor tested Gulacsi with an angled strike after a dozen minutes but missed the target with a free-kick.
The Merseysiders doubled their lead on 26 minutes with a fine strike from the edge of the box by Charlie Barnett from Ryan Shotton's pass, after good work by Ed Sonko.
United managed their first shot on target after 38 minutes with a Marc Pugh effort following a free-kick beaten out by Danny Coyne.
Gareth Edds replaced Steve Jennings in midfield in the second half for Tranmere and they remained in cruise control despite a more determined looking Hereford.
Gulacsi did well to block out a low drive from Moore and as play swept the other end, Coyne turned a Stephen O'Leary header away for a corner.
Hereford grabbed a consolation goal in the last minute of added time. Steve Guinan fired home from the penalty spot after Shotton tripped Jennison Myrie-Williams in the box.
Done, Pugh and Kris Taylor tried hard for the losers. Savage and Moore were always dangerous up front for Tranmere, with Shotton and Ben Chorley giving little away in defence.