Struggling Hereford surprised their high-riding opponents with a series of attacks in the early stages when Pugh twice had goalkeeper Shwan Jalal saving.
Jalal, however, was lucky when he dropped a cross from winger Mark Marshall but central defender Jason Pearce hacked the ball away to safety. Marshall then had a clear-cut opening midway through the half but failed to find the target with only the keeper to beat.
Down at the other end, Scott Guyett went close to putting Bournemouth in front with a powerful header while Lee Bradbury had a shot pushed against the foot of a post by Adam Bartlett.
But Hereford eventually went in front in the 50th minute when Pugh beat Jalal with a low shot from close range.
Bournemouth levelled 10 minutes later when Steve Fletcher turned in the area to shoot past Bartlett for an equaliser. But Pugh struck again to snatch the points in the 77th minute when he lashed the ball into the far corner of the net from 12 yards.