Huddersfield had plenty of openings but lacked the quality up front which Martin showed when he headed his third goal in four games before setting up substitute Johnny Russell for the second.
Both teams had chances from the start as first Harry Bunn saw a shot cleared off the line by Cyrus Christie with Scott Carson beaten before Nick Blackman fired wide from 10 yards when Tom Ince crossed from the left.
Huddersfield were moving the ball through the midfield with confidence and they caused panic in the Derby defence in the 11th minute when Joe Lolley’s low cross from the right was sliced onto the roof of his own net by skipper Richard Keogh.
Derby responded instantly when Ince came inside and went past two Huddersfield defenders only for Dean Whitehead to get across and make a vital tackle as the winger was poised to shoot.
The home side were allowing Huddersfield too much space through the middle and they were almost undone when Lolley slipped into the box only to get the ball caught under his feet.
But the visitors were almost punished for giving the ball away when former Huddersfield star Jacob Butterfield pounced on a loose pass to send Ince in on the left and his shot was deflected against the outside of Jed Steer’s left post.
With sleet falling over the iPro Stadium, the afternoon got distinctly chillier for Huddersfield in the 31st minute when Christie crossed from the right and Martin got above Mark Hudson to head low past Steer’s outstretched right hand.
Hudson’s angry reaction showed he should have done better but Huddersfield reminded derby they were still in the game when Carson had to dive to his left to beat out a Jamie Patterson shot.
Patterson had a great chance to level three minutes into the second half when Tommy Smith’s cross was laid off by Nahki Wells but the midfielder shot wide from 12 yards.
Smith was involved again a minute later when his low shot was pushed away by Carson and Wells got into a good position inside the area without getting a shot away.
Huddersfield were increasingly getting into dangerous areas but Derby had a chance to extent their lead on the hour when Ince got in on the right but his tame shot was easily saved by Steer who did well a minute later to parry a fierce Martin drive.
Ince struck the bar from 20 yards but Derby got a second goal in the 73rd minute when Martin teed up Russell on the right edge of the area and he bent a shot into the bottom corner to end Huddersfield’s challenge.
Huddersfield head coach David Wagner, though, saw plenty of encouragement in his team’s display.
“At the end we had no complaints with the squad, they tried everything and worked unbelievably hard,” he said.
“Derby had to produce one of their best performances today to be able to beat us and so we can leave the stadium with our head up. I think there were only some small key points that decided this game and those were in Derby’s direction which is why we lost.
“It’s important that you trust and believe in yourself and sometimes you get what you deserve and sometimes not. Today I think we didn’t get what we probably deserved, which was a draw or maybe more.
“We missed something today, and not for the first time, but we will find the answer to this question and if we can do that we will react in the summer (transfer) window. They had a good chance and scored, we shot 10, 12 times from the box and didn’t score.”
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