County manager Craig Short, who was appointed as Steve Cotterill's successor in June, saw his side's defence exposed on numerous occasions during his first competitive match in charge.
Huddersfield should have opened the scoring after 25 minutes when a quick counter-attack put Joe Garner clean through, but the Nottingham Forest loanee shot wide.
However, the Terriers made amends seven minutes later when Pilkington rifled a shot into the top corner from an acute angle.
Jordan Rhodes, who netted 19 league goals last term, doubled Town's advantage soon after when he latched onto Garner's pass and calmly slotted the ball home.
County, who lost just one league game at Meadow Lane on their way to the title last term, saw Liam Chilvers' goalbound volley blocked by Garner who then himself hit the bar at the other end.
And Huddersfield put the result beyond doubt 17 minutes from time through Pilkington's sweetly struck shot from the edge of the area.