Theo Robinson's early goal proved enough to see Derby through to the FA Cup fourth round at the expense of Championship rivals Crystal Palace.
Robinson slotted home at the second attempt in the ninth minute after Palace goalkeeper Lewis Price had parried his initial close-range effort.
Price then produced a string of saves to keep Palace in the game.
The south Londoners rallied late on but Calvin Andrew's header over the bar was as close as they came to an equaliser.
The result was hardly a surprise, given the discrepancy between the two sides' teamsheets.
Derby had 11 shots on target to Crystal Palace's two at Pride Park
Derby fielded the same line-up from the 1-0 victory over Hull on Monday, but Palace - with one eye on Tuesday's Carling Cup semi-final first leg clash with Cardiff - made seven changes to the side that lost to Leicester last time out.
After giving his side an early lead from Jamie Ward's cross, Robinson, who also scored the winner against Hull, came close to making it 2-0 but his 25-yard strike produced a fine save from Price.
Ward then missed the target by a whisker from a similar distance, while another long-range effort from the striker was fumbled by Price, but no one could capitalise.
In between Ward's efforts, Palace came close through Antonio Pedroza but his strike from just inside the area narrowly missed the right-hand post.
Callum Ball missed presentable chances for Derby either side of half-time and Craig Bryson almost found himself through on goal but could not quite latch on to Robinson's ball.
Soon afterwards, Price had to be at his best to tip over Paul Green's header at the back post from Ward's corner.
Despite being only one point and two places behind Derby in the Championship, Palace were outclassed, their minds clearly on Tuesday night.
Derby County manager Nigel Clough told BBC Radio Derby:
"We weren't as sharp as we've been in the last three games, but it's another win, another clean sheet and we're in the hat, so it's job done.
"It was a bit more difficult than the last three. We were watching the Palace lads coming off and the one thing they were was fresh. They hadn't played much football over Christmas.
"They had a lot of young lads and they had a chance to come and play at a lovely stadium. It's sometimes harder when we've come in on the back of three very difficult games."
Crystal Palace boss Dougie Freedman told BBC London 94.9: "
We just missed out. We gave everything we had but we just came up short. I gave youngsters debuts today, and it just shows you that what we do at Crystal Palace - we give people opportunities.
"I am very proud of the way they handled themselves especially after the goal went in. They were tested and they stood up to the challenge. The character they showed today was second to none.
"I think credit to our lads. They gave it a right good go and they put Derby under a lot of pressure but in the end we couldn't quite get the goal."
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