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:
13. SUBS
Scott Banks, Andy Lyons, Lee Evans, Jordan Brown (All 7/10), CJ Hamilton (N/A). Photo: Gareth Evans