The Millers twice came from behind as they won their second game of the week following their victory against Bournemouth in midweek.
Swindon were lucky to only concede three goals as they produced a poor defensive performance.
In addition to conceding three goals Swindon owed a big debt to goalkeeper Rhys Evans who twice came off best in confrontations with Paul Shaw and Butler when the strikers were played clear.
Swindon, who have also been recovering from a poor start to the season, went ahead in the 20th minute when Rotherham goalkeeper Gary Monkhouse fumbled a centre from the left by Andy Nicholas under pressure from striker Lee Peacock.
Jamie Cureton was the first to respond as he headed into an empty net from six yards out.
But Swindon never looked likely to hold on to their lead and a minute later Butler was picked out at the far post to score with a ten-yard left-foot shot.
Swindon were ahead again in the 25th minute when a free-kick by Peacock got through the defensive wall and struck goalkeeper Monkhouse on his line.
Ricky Shakes got the ball back into the danger area and Sean O'Hanlon prodded in from two yards for his fifth goal of the season.
Rotherham were back on terms in the 30th minute with another simple goal, this time a free-kick on the edge of the area by the dominant Lee Williamson was met at the far post by the unmarked Shaun Barker who headed home unattended.
Butler's winner came as the result of more chaos in the visitors defence when a long throw from Barker bounced over everyone to allow Butler's looping header to arch into the net.
Monkhouse made up for his earlier error by making three saves to preserve the points for Rotherham.
He kept out a free-kick from Andy Gurney and also denied substitute Albert Jarrett and Cureton with eight minutes remaining.