On a windy afternoon in the Potteries, Brogan came off the bench for the injured Kevin Ellison to net his first goal since recovering from a double leg fracture19 months ago.
Nicky Law then bagged the points in a grandstand finish after Vale had levelled it up before half time.
The game got off to a crisp start with Rotherham doing most of the early attacking and forcing a succession of corners.
Ellison was first to test home keeper Chris Martin and had the best early chance on 10 minutes as he fired his left foot drive into the Millers fans.
Five minutes later though Ellison limped off with what appeared to be a foot injury and was replaced by Brogan, who opened the scoring on the half hour as he headed in Dale Tonge's pinpoint right wing cross.
The Millers nearly extended the lead as Adam Le Fondre's turn and shot from 20 yards was tipped over the bar by Martin shortly afterwards.
Vale hit back and equalised on 36 minutes as Luke Prosser beat Andy Warrington at the back post to level matters.
Just before half time a fairly quiet affair suddenly sprung into life with a flurry of yellow cards and tough tackles, the second of which came for goalscorer Prosser as his trip on Le Fondre 25 yards from goal saw him sent for an early bath.
The Millers came up against a stubborn home outfit after the break and created little in the way of clear cut goalscoring chances, whilst always looking in control.
Law came closest to restoring the advantage with 20 minutes left but his shot from the right corner of the box whistled wide whilst the hosts' Marc Richards wasted a glorious chance to give Vale the lead.
But Law was to be the hero in the second minute of stoppage time, as he jinked into space to smash home from just inside the area past Martin to give the Millers the spoils.