The visitors had failed to score in their previous five matches but took just seven minutes to land the decisive blow and wreck Vale's unbeaten home record.
Mike Jones fired a hopeful shot from 20 yards and Ryan Lowe's outstretched leg made a decisive contact to wrong-foot Vale goalkeeper Chris Martin.
Vale did make most of the running in the first half and almost levelled in the 18th minute when a shot from Louis Dodds drew a fine save from Wayne Brown.
But Bury began to defend with increasing composure and then enjoyed their best period of pressure at the start of the second half.
Jones came within a few inches of extending their lead in the 54th minute when his right-foot shot struck the base of the far post.
And Andy Bishop had an effort blocked by John McCombe before Vale began to exert some late pressure.
Bury defender Ryan Cresswell was sent off two minutes from time, but Vale could not find a way through despite five minutes of stoppage time.