The striker grabbed three second-half goals to confirm the Yorkshire side's first Saturday win since May 2004.
It was no more than Mick Harford's side deserved after controlling the game from start to finish leaving Colin Hendry's Seasiders looking for their first league win of the season.
The home side went ahead in the 40th minute. A long throw from Shaun Barker was half cleared and fell to John Mullin who crashed in a close-range shot for his first goal of the season.
Blackpool's only early chance came when midfielder John Doolan lashed a goalbound 25-yard shot that was deflected out for a corner.
But immediately after Rotherham forged in front, Blackpool came close to an immediate reply when Peter Clarke went close with a header.
But the home side saw a golden chance to stretch their advantage go begging seconds before the break.
Clarke handled in the area when Burton produced a clever shot but striker Martin Butler saw Les Pogliacomi save the spot-kick low to his right.
A desperate challenge from Clarke again handed Rotherham a second penalty after 58 minutes.
He bundled over Burton in the area and the striker stepped up to take the spot-kick himself slotting in a low shot.
Two minutes later David Worrell burst down the right and whipped in a testing cross and Burton produced a powerful header to put the game beyond the visitors.
Blackpool came close to a consolation goal after 76 minutes when Keigan Parker headed a Keith Southern cross and beat Neil Cutler only for the ball to hit the foot of the post.
Burton rounded off the afternoon five minutes from the end when he smashed in a shot from 18 yards after Paul McLaren cut back a clever pass into his path.