Paul Peschisolido made a dream debut for Derby as he capped an inspired performance with the winning goal.
The Rams dominated the opening 45 minutes but were unable to make their
superiority count against a gritty Rotherham outfit.
Peschisolido grabbed the breakthrough at the second attempt after his first effort was kept out by Mike Pollitt.
The forward could have added a second and Tom Huddlestone also went close as the Rams finished strongly.
George Burley's side bolstered their squad this week by signing defender Jeff Kenna from Birmingham and Peschisolido from Sheffield United.
Both were thrown straight into the starting line-up.
Rotherham's Julien Baudet cleared an early corner from Candido Costa and Chris Swailes then blocked a piledriver from Huddlestone as the home side started strongly.
Peschisolido sent a fifth-minute shot wide as Derby dominated the early exchanges.
Rotherham's attacking forays were limited and a Darren Garner cross was easily cut out by Derby keeper Lee Grant on one of the few occasions they looked threatening early on.
The home side looked much more impressive with Pollitt having to punch clear from a Costa free-kick and Peschisolido having another goalbound effort blocked.
Rotherham's Paul Warne tried his luck from distance, but his effort 10 minutes before the interval was too high.
The home side continued to push for the opener with Lee Holmes sending a shot wide of the target and Peschisolido and Huddlestone both having efforts on goal in quick succession.
Peschisolido then brought a fine save out of Pollitt after 57 minutes as the visitors somehow clung on.
But it proved a brief respite as Derby deservedly took the lead on the hour through Peschisolido.
Richard Jackson received the ball on the right and his cross found the former Sheffield United striker who lashed the ball home on the rebound after his initial effort had been kept out by the over-worked Pollitt.
Peschisolido went agonisingly close to adding a second just seven minutes later, but his left-footed curler was superbly saved by Pollitt.
Pollitt distinguished himself again in injury-time with another superb save to deny Huddlestone.
Derby: Grant, Kenna, Mawene, Johnson, Jackson, Costa, Taylor,
Huddlestone, Osman, Paul Peschisolido, Paul Peschisolido,
Tudgay. Subs: Oakes, Boertien, Holmes, Labarthe Tome, Whelan.
Rotherham: Pollitt, Stockdale, Gilchrist, Richard Barker,
Hurst, Garner, Minto, Baudet, Swailes, Butler, Warne. Subs:
Montgomery, Proctor, Daws, Hoskins, Mullin.
Referee: A Leake (Lancashire).