Manager Nigel Clough made wholesale changes to his side to rest players ahead of Sunday's FA Cup semi-final against Hull.
But the Blades still won the game courtesy of Ben Davies' last-minute penalty, awarded after Rotherham skipper Craig Morgan tangled with Harry Maguire at a corner.
"They were excellent. We made eight changes from the team on Saturday because we've got a massive game coming up on Sunday," said Chris Morgan after the 1-0 victory at Bramall Lane.
"The young lads have been doing excellent in the under-21s and the under-18s so we gave them a chance.
"I think a lot of credit has to go to the academy coaches we've got who work with them day in, day out.
"I thought the young lads stood up to the challenge of Rotherham. They're a physical team and we had to deal with it. It was a fantastic performance and a great result.
"It was a typical Yorkshire derby, but in the heat of the battle our players put their foot on the ball and played.
"We've got a good squad and it was pleasing to see the young players stand up to the test with the senior players helping them along.
"I think it was a penalty. We could see it clearly from our technical area and he got hold of Harry and pulled him down."