After Wednesday's Jermaine Johnson had an early effort blocked and Marcus Tudgay headed over, Jordan Rhodes went desperately close to putting Huddersfield in front with a shot from inside the penalty area which struck the woodwork.
The visitors did take the lead in the 23rd minute when Carey beat Nicky Weaver with a superbly-flighted free-kick over the defensive wall.
Wednesday threatened to make a quick response when Johnson made a good run into the area and fired at goal, but his effort was beaten away by goalkeeper Ian Bennett.
Pilkington put Huddersfield further ahead in the 34th minute, finding the net with a fine finish after receiving a square pass from Joe Garner just outside the area.
The lively Rhodes failed to hit the target from inside the area just before the break and there were few chances at either end in the second-half. Wednesday substitute James O'Connor had a low shot comfortably saved, while Pilkington tested Weaver with a long-range effort.