The hosts completely dominated the first half but had to wait until two minutes before the break to take the lead.
They racked up three corners in the first three minutes and Ryan Cresswell – back for his first start since last September – just failed to get a foot to the second and then headed over from the third.
Ben Pringle had a shot brilliantly saved by David Cornell and Alex Revell headed over from Lewis Grabban’s cross.
But the breakthrough came in the 43rd minute. Sam Wood’s cross from the left looked comfortable for Cornell, but Grabban nipped in front of him to nod the ball over the keeper and into the empty net for his 19th of the season.
Hereford’s only serious challenge on the Rotherham goal was a Richard Peniket header which just cleared the bar. By comparison, the second half was a very tame affair. Rotherham went close, Revell firing just wide, but they failed to press home their advantage and Hereford simply could not find a way through.