Tom Hitchcock and Jerry Yates both scored two goals apiece, whilst Nicky Walker was also on the score-sheet.
The Stags were forced to make a late change to their starting xi as Paul Black suffered a knock in the warm-up and had to be replaced at left-back by teenager Conor Green.
Rotherham created the first opening after six minutes when West Thomas latched onto a through ball, but his low effort was comfortably saved by Ian Deakin.
The Millers thought they should have been awarded a spot-kick on 22 minutes, when Michael O’Connor burst through on goal and was barged over by Darryl Westlake on the edge of the area.
Referee Gary Rhodes opted to award a free-kick rather than a penalty, and O’Connor’s subsequent set-piece went through the Stags’ five-man wall, it sailed wide of Deakin’s right-hand post.
The Stags’ custodian and youngster Jack Thomas also required treatment in what was a physical first half, which had very few other goalscoring opportunities of any note.
However, Rotherham dominated after the re-start and went close again on 55 minutes, when O’Connor curled a 30-yard free-kick narrowly over the target.
Green produced a perfectly-timed last-ditch challenge to foil Wes Thomas only a few moments later, as the Milles continued to press forward with intent.
The South Yorkshire side eventually made a breakthrough on the hour mark when Thomas’ ball into the area reached Walker, who found the target from six yards.
The floodgates soon began to open as Hitchcock quickly made it 2-0 with an emphatic close-range finish, despite Deakin doing well to initially deny Walker.
Walker was the Stags’ chief tormentor and had a low 30-yard attempt well-saved by Deakin on 69 minutes, before he played a significant part in the Millers’ third goal.
The midfielder played an inch-perfect pass from the right flank towards substitute Yates at the back-post, who was left with a simple, close-range tap-in.
Yates enjoyed a great afternoon as he made it 4-0 with less than 10 minutes remaining, this time as he re-adjusted his body well to reach O’Connor’s right-wing cross and head past Deakin.
The Millers were now in full control and completed the scoring with on the brink of stoppage-time, when Hitchcock hammered the ball home at the near-post, following a corner.
Team: Deakin, Green, Westlake, McKenzie (Spencer), Marsden, Stevenson, Clements, Briscoe, J.Thomas, Dyer (Lamb), Trialist (Hemagou).