Within five minutes they were two down, 17 minutes on Rovers were three-up and it all became a rout.
Hereford's misery began as Darryl Duffy, Rovers' £100,000 signing from Swansea City, chased down a long ball and defender Dean Beckwith fell over. The keeper got an arm to Duffy's sharp shot but had no chance of keeping it out of his net.
Failure to mark Rickie Lambert cost Hereford a second goal minutes later as the striker picked his spot with an accurate bending shot which caught Craig Samson on the wrong side of his goal.
The Rovers front pair combined for the third goal, Lambert slipping a short pass for Duffy on his right to lash in a powerful right-foot drive.
Between his goals, Duffy had raced passed a hapless defence, only to see his shot bounce off a post.
Heads could have gone down, but lifted by Simon Johnson's non-stop running and on-target shots from Ben Smith and Toumani Diagouraga, the Bulls were always threatening to strike back, but simply couldn't live with their mistakes.
Their half-time break was cut short for an extra keep-warm spell, but 30 seconds after the restart the game was even more decisively Rovers.
Jeff Hughes, a summer signing from Crystal Palace, swept past Hereford's right-back Richard Rose as if he wasn't there to thunder a shot high into the net.
Hereford finally realised this was never going to be their day when lively sub Bradley Hudson-Odoi saw a shot blocked on the line by Aaron Lescott and was then denied a goal by a very tight offside decision.
Twenty-five-yard free-kicks late on from Lambert and Chris Lines underlined Rovers' superiority, before Steve Guinan knocked in a consolation goal in added-on time.