Derby's recent dominance over Leeds continued as Jamie Ward's second-half strike earned the Rams a sixth straight win over the Whites.
Ward, who hit the post in the first half, fired in from close range after United keeper Andy Lonergan parried his initial effort.
Robert Snodgrass went closest for Leeds but his free-kick was was tipped over by Rams keeper Frank Fielding.
The result leaves Leeds without a win in three games.
United's manager Simon Grayson was marking three years in charge of the Elland Road club on Boxing Day but his side struggled to make it a happy celebration.
Fielding was equal to Ross McCormack's 35-yard effort while the Rams stopper also denied Snodgrass and beat away a drive from Danny Pugh.
However, the visitors created little else and they found themselves behind when Ward tucked in to his third of the season after Lonergan failed to hold his first shot.
Fielding made a late double save to deny McCormack and Adam Clayton to ensure Derby recorded just their second win in nine games.
Derby manager Nigel Clough: "I thought the performance, all round, was a proper team one. The players were fighting for each other against one of the strongest sides in the division.
"It's ironic that we had more defending to do than in the last four games, and that's the one where we've kept a clean sheet.
"The players knew it (pressure) was coming and would have to deal with it, and did. It was a good, old-fashioned Boxing Day ding-dong with a lot of effort and endeavour."
Leeds manager Simon Grayson: "[There is] always pressure as manager of Leeds United and expectancy from everybody. I put pressure on myself.
"Ken Bates has given me three years so far, two years more than most managers get throughout the country. We're still in the top half, ready to kick on.
"I know what's required at this football club because it means a lot to me and I'll be doing my best to get us to kick on.
"I've had meetings with Ken Bates and identified the targets we'd like to bring in and hopefully we can once the window opens."