THE only good news for Rotherham United after this loss is that they remain just one point shy of safety following fellow strugglers Millwall’s defeat at Elland Road.
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).