The 24-year-old midfielder powered home an unstoppable shot from the edge of the penalty area in the fifth minute and doubled Brighton's lead five minutes before half-time with a clinical low finish.
Simon Church, on loan from Reading, struck a consolation for Huddersfield in the final minute in his second game for the club, but it was too little too late for Simon Grayson's side, who slipped to a third home league defeat of the season.
Brighton were good value for their fourth win on the road against an out-of-sorts Huddersfield, who struggled to create chances against a well-drilled Brighton defence.
Buckley wasted little time adding to his three goals for the season in some style, giving Brighton a fifth-minute lead when crashing the ball high into the roof of the net after taking Bruno Salter's neat pass inside on the edge of the penalty area.
Barnes spurned a golden chance to put the visitors two-nil up twice in quick succession 10 minutes later, first dragging his low shot from the edge of the box just wide and then heading Andrea Orlandi's corner over the crossbar.
Striker Church, in his second game for the Terriers after joining last week on loan from Reading, headed inches over the crossbar before Brighton stunned the home crowd with a second goal in the 40th minute.
Craig Mackail-Smith played the ball inside the area from the right and Buckley arrowed a low shot from 12 yards across Huddersfield goalkeeper Alex Smithies and into the bottom corner.
Huddersfield started the second half with more purpose, but found clear-cut chances hard to come by and it was not until the 59th minute that Lee Novak threatened with a low angled shot from inside the area.
Brighton went close to adding a third goal in the 74th minute, but Buckley, whose goalbound shot from the left side of the penalty area was brilliantly turned away at full stretch by home goalkeeper Alex Smithies, was denied his hat-trick.
Church converted Ward's ball in from the right from close range in the 90th minute, but Brighton comfortably held on without any further scares to take maximum points.