Bas Savage and Charlie Barnett netted first-half goals as the home side recorded their 15th home win of the season and left Hereford 12 points from safety with just four games remaining - and a far inferior goal difference.
It took the Merseysiders just eight minutes to take the lead with a fine finish by Savage when set free by Ian Moore.
Rovers were well on top and it was no surprise when they doubled the advantage after 26 minutes when Barnett found the top corner from the edge of the box after good work by Ed Sonko and Ryan Shotton.
Hereford got a consolation with the very last kick when Steve Guinan converted a penalty after Shotton was judged to have tripped Jennison Myrie-Williams inside the box.
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