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The Scotland international struck a 25-yard shot into the top left corner in the 39th minute and Derby could have won by a bigger margin with better finishing.
This was their first victory back in the top-flight and it was thoroughly deserved, although Newcastle will feel they also had their chances.
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Derby had gone into the game on the back of four consecutive defeats but they started positively and self-confessed Magpies fan Steve Howard headed over from a corner after only 53 seconds.
But it was Newcastle who should have gone in front in the 18th minute when James Milner broke on the left and slipped the ball through to Michael Owen who, after rounding Stephen Bywater pulled the ball back, but David Rozehnal shot wide of the empty net from only ten yards.
It was a dreadful miss and his team were made to pay a high price when Bywater launched a long kick downfield and Howard laid the ball into the path of Miller, whose first-time shot sailed over Steve Harper and into the net.
But Newcastle could have levelled before half-time when Milner played Shola Ameobi in on the Derby left, but he shot wastefully wide.
The second period saw Derby cling fiercely to their lead as Newcastle pressed, although there was little creativity from Sam Allardyce's team.
The better chances fell to Derby, with Howard twice heading wide from unmarked positions as the home side played on the break.
The biggest moment of danger to the Rams came when Obafemi Martins turned Tyrone Mears just outside the area, forcing the full-back to drag him down and pick up a yellow card.
But the free-kick hit the top of Derby's defensive wall and went behind and although the home fans had to endure four minutes of stoppage time, Newcastle never looked like equalising.