For most of the first half it seemed they were destined to stay in deficit as they played second fiddle to managerless Grimsby.
The Mariners were the better side in that first half and put themselves on course for a first win of the season when midfielder Danny Boshell fired them in front on 29 minutes.
It was a superb strike from 20 yards and it gave Andy Warrington no chance as it found the far top corner.
Alex Rhodes set up the opportunity with an inch-perfect cross to the far post which Reid powered home.
Rotherham simply got stronger and stronger after that boost and on 57 minutes, Mark Hudson fired his first goal of the season, although ex-Millers goalkeeper Phil Barnes would've been disappointed in the way the ball squeezed under him at the near post.
Sub Richie Barker, who returned to the club he left four years ago on Friday, marked the moment with a typical far post header ten minutes from time from another pinpoint Rhodes centre to put the seal on the afternoon.