Hylton took his tally in this season's competition to seven with a first-half double and a third in the 62nd minute before Lee Frecklington pulled one back from the penalty spot after 71 minutes.
Kari Arnason picked up a second yellow card after 83 minutes to kill off the Millers' fightback only for Hylton to ruin his perfect day with a straight red card a minute later.
But after reaching the fourth round for the first time in the club's history, Holdsworth was in no mood to be downbeat.
"It's created history for the football club. We asked the players to be a part of that," he said.
"We said that no-one will ever be able to take that away from them. When you create those moments, it's fabulous and special.
"It was not just about the performance, it was about the way we went about the business. We took our goals really well and Danny (Hylton) was clinical. That sort of finishing is what we see in the Championship week in, week out.
"We went through a rough spell but that was earlier in the season. We've turned the corner now. We've got four defeats in 14 games.
"The players are playing with confidence and that showed. You don't beat Rotherham without passion and desire. We had all of that. We knew they were going to give everything they've got and we had to be the same.
"We've got a good financial reward for the club which is much needed and we can build on this result."
- Sports & Recreation
- Lee Frecklington