Josh Bowler broke the deadlock after just 10 minutes, with a curling effort from the edge of the box sneaking past Cameron Dawson on the edge of the box.
Ian Evatt’s side swiftly doubled their lead, as Danny Imray scored against Rotherham for the second time this month.
The ball was worked to the wing-back down the right side, with the Crystal Palace loanee drilling himself into space before firing a shot across the face of goal.
In a rare moment of concern for the Seasiders ahead of the break, Bailey Peacock-Farrell was on hand with a quick reaction save to deny Denzel Hall from close-range.
Following the restart, Rotherham did have the ball in the back of the Blackpool net, but had their celebrations cut short by the linesman’s flag.
Things quickly got worse for the visitors ahead of the hour mark, with Baptiste being shown a straight red card.
The Seasiders quickly made the most of this advantage, as Ashley Fletcher finished past Dawson with the outside of his boot.
In the closing stages, Tom Bloxham was able to added his name to the scoresheet as well, as he fired one into the bottom corner to round off an impressive evening.
Here’s how the Seasiders performed:

1. How did the Seasiders perform?
Blackpool took on Rotherham United at Bloomfield Road. Photo: Gareth Evans

2. Bailey Peacock-Farrell - 8
Bailey Peacock-Farrell made a quick reaction save to deny Denzel Hall from close-range ahead of the break. Photo: Gareth Evans

3. Olly Casey - 8
Olly Casey is looking more and more at home in a back three, and we're starting to see some different sides to his game. Photo: Gareth Evans

4. Fraser Horsfall - 8
Fraser Horsfall produced another confident display at the back. Photo: Gareth Evans

5. James Husband - 8
It was another solid evening for James Husband on the left side of the back three, with even a bang to the head in the first half not deterring him. Photo: Gareth Evans

6. Danny Imray - 9
Like the meeting between the two teams earlier in the month, Danny Imray caused nightmares for Rotherham, and bagged himself another goal against them. Photo: Gareth Evans