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:
7. George Honeyman - 8
It was a tenacious display from George Honeyman in the centre of the park, with the midfielder winning the ball back on several occasions. Photo: Gareth Evans
8. Albie Morgan - 8.5
Albie Morgan was majestic at times in the centre of the park, and kept the Seasiders ticking at times. Photo: Gareth Evans
9. Josh Bowler - 8.5
It was a bit of brilliance from Josh Bowler for the opener, with the midfielder catching out Cameron Dawson with a well-taken shot on the edge of the area. Photo: Gareth Evans
10. Zac Ashworth - 8
Zac Ashworth offered his usual defensive stability down the left side as wing-back. Photo: Gareth Evans
11. Ashley Fletcher - 8.5
Ashley Fletcher was on hand to assist Danny Imray, before claiming one of his own in the second half. Photo: Gareth Evans
12. Tom Bloxham - 9
Tom Bloxham had several bright bursts, and was rewarded with a goal and an assist. Photo: Gareth Evans