Derby moved back into the play-off spots and left Rotherham in the bottom three after a six-goal blitz.
Mason Mount marked his comeback after two months out by winning the 13th-minute penalty Martyn Waghorn dispatched before Bradley Johnson headed in the 39th-minute second.
Waghorn headed his second three minutes later and victory was assured when Mount struck in the 48th minute.
Richard Wood headed in a corner but Mount’s header set-up Duane Holmes before Waghorn completed a hat-trick with his second penalty after Tom Lawrence was tripped by Marek Rodak to give Derby six goals in a game for the first time since 1996.
Rotherham manager Paul Warne said: “I think we played Derby on a good day and we are missing four key players. We’ve got a small squad although I still expected a bit more out of the team but maybe I picked the wrong team or did the wrong things so I have to look at myself.
“No-one likes to lose heavily but, at the start of the season, Brentford gave us a good licking and we bounced back so it might reset everybody.
“I believe it will have some psychological harm for a couple of days but on Monday we’ll be there to pick them up again so I hope they hurt over the weekend because it’s certainly ruined mine but I don’t think it will have long-term damage.”
Derby County: Roos, Bogle, Keogh, Tomori, Malone (Cole 76), Holmes, Johnson, Mount (Bennett 76), Harry Wilson, Waghorn (Marriott 81), Lawrence. Unused substitutes: Carson, Wisdom, Bryson, Huddlestone.
Rotherham United: Rodak, Vyner, Ihiekwe, Wood, Jones, Ajayi, Taylor (Towell 46), Williams, Wiles (Crooks 46), Newell, Yates (Forde 78). Unused substitutes: Palmer, Price, Smith, Kayode.
Referee: T Robinson (West Sussex).