Winger Matt Ritchie scored two first-half goals in a minute to help Swindon to victory at Rotherham.
His first was a left-footed volley and the second, from almost an identical spot, took a deflection on its way past Rhys Taylor.
Alex Revell, who headed just wide in the first half, closed the gap with a header from Chris Holroyd's left-wing cross after the break.
Lewis Grabban almost got the equaliser but hit the post with 17 minutes left.
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Rotherham United manager Andy Scott told BBC Radio Sheffield:
"If you don't perform for 90 minutes against good sides you don't deserve anything.
"It's too easy to play well and chase a game and you've got to have some heart and desire to go and take it to them from the start.
"We had a great opportunity today, we'd done a lot of work on Swindon, went and watched them on Tuesday, they played exactly how I knew they were going to play - people behind the ball, they were going to counter attack.
"We knew we had to attack down the wings, we knew there was going to be space down the wings for our full-backs to drive into. And yet we get to 45 minutes and we haven't done it."
Swindon Town manager Paolo di Canio told BBC Wiltshire:
"Fantastic win in the way it came because in the last 20 minutes they [Rotherham] pushed hard.
"To play 40 minutes under pressure wasn't easy but they [Swindon players] have been warriors.
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