Will Buckley marked his return for Brighton with two first-half goals to help his side leapfrog Huddersfield into seventh place in the Championship.
Buckley gave the visitors a fifth-minute lead with an unstoppable shot from the edge of the area.
Their advantage was doubled when Buckley arrowed a low shot from 12 yards into the bottom corner.
Simon Church converted Danny Ward's 90th-minute cross from close range, but Brighton comfortably held on.
It was a third home league defeat of the season for Simon Grayson's side as Brighton secured a fourth win on the road.
Buckley wasted little time adding to his three goals for the season, crashing home a high finish after Bruno Saltor's neat pass.
Ashley Barnes spurned two chances to extend the lead, first dragging his low shot from the edge of the box just wide and then heading Andrea Orlandi's corner over the bar.
Huddersfield had to wait until the 25th minute for their first effort on goal as Adam Clayton fired wide from 30 yards.
Church, in his second game for the Terriers after joining on loan from Reading, headed just over the bar before Brighton struck again.
Craig Mackail-Smith played the ball in from the right and Buckley finished across Alex Smithies and into the bottom corner.
Huddersfield started the second half with more purpose, but found clear-cut chances hard to come by until Lee Novak headed wide.
Brighton went close to adding a third but Buckley's goalbound shot from the left was brilliantly turned away at full stretch by Smithies before Church's late strike for the hosts.
Huddersfield manager Simon Grayson:
"You always know Gus [Poyet's] teams are going to be composed and we probably contributed to our own downfall by not getting at them.
"It's a learning curve for us and I have told the players that when we lose matches we have to understand why we've lost so we can get better.
"Brighton have spent some money over the last couple of years with players like Mackail-Smith and Buckley, and if they are not thereabouts at the end of the season they will be disappointed."
Brighton manager Gus Poyet:
"Three hours ago we were one win in nine and people were saying that was terrible.
"Now they are saying we are unbeaten in five and it's fantastic.
"We are a good team and difficult to play against. I am happy for the players.
"Sometimes football is fair and you get three points but other times you have to take it on the chin and go home.
"We have had to battle and some of our players are not used to that type of football. It's a learning curve."
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +2:51
Will Buckley takes a shot. Save by Alex Smithies.90:00 +1:32 Booking
Booking The referee books Inigo Calderon for time wasting.89:37
Assist on the goal came from Daniel Ward.89:37 Goal scored
Goal! - Simon Church - Huddersfld 1 - 2 Brighton A goal is scored by Simon Church from close range to the bottom left corner of the goal. Huddersfield 1-2 Brighton.88:30
Foul by Dean Hammond on Scott Arfield, free kick awarded. Alex Smithies takes the free kick.87:54
Unfair challenge on Will Hoskins by Joel Lynch results in a free kick. Free kick taken by Bruno Saltor.86:42
Daniel Ward takes a short corner, clearance made by Will Buckley.85:58
Outswinging corner taken from the left by-line by Daniel Ward, Gordon Greer makes a clearance.85:19
Foul by Will Buckley on Joel Lynch, free kick awarded. Joel Lynch restarts play with the free kick.84:16
Free kick awarded for a foul by Peter Clarke on Dean Hammond. Andrea Orlandi takes the free kick.83:53
Daniel Ward takes a shot. Save made by Peter Brezovan.82:45
Adam Hammill crosses the ball, Peter Brezovan makes a save.81:12
Outswinging corner taken from the left by-line by Daniel Ward, Bruno Saltor makes a clearance. Corner taken right-footed by Daniel Ward from the right by-line, Gordon Greer manages to make a clearance.77:12
The free kick is delivered left-footed by Andrea Orlandi from right channel, Alex Smithies makes a save.77:12 Booking
Booking Joel Lynch is cautioned.77:04
Free kick awarded for an unfair challenge on Liam Bridcutt by Joel Lynch.75:16 Substitution
Substitution Scott Arfield joins the action as a substitute, replacing Oliver Norwood.74:37 Substitution
Substitution Inigo Calderon comes on in place of Marcos Painter.73:58
Will Buckley takes a shot. Save by Alex Smithies. Corner taken short by Andrea Orlandi.
Effort from outside the penalty area by Simon Church goes wide left of the goal.69:41
Will Buckley takes a shot from long range which goes wide of the right-hand post.66:43 Substitution
Substitution Alan Lee is brought on as a substitute for Lee Novak.66:43 Substitution
Substitution Keith Southern goes off and Adam Hammill comes on.66:24 Substitution
Substitution Will Hoskins joins the action as a substitute, replacing Craig Mackail-Smith.64:35
Foul by Peter Clarke on Craig Mackail-Smith, free kick awarded. Liam Bridcutt takes the free kick.63:57
Headed effort on goal by Lee Novak from inside the penalty box misses to the right of the goal.62:50
Bruno Saltor challenges Lee Novak unfairly and gives away a free kick. Strike on goal comes in from Adam Clayton from the free kick, blocked by Liam Bridcutt.62:07
Corner taken left-footed by Daniel Ward, clearance made by Marcos Painter.60:10 Substitution
Substitution Gary Dicker joins the action as a substitute, replacing Ashley Barnes.59:07
Oliver Norwood challenges Dean Hammond unfairly and gives away a free kick. Direct free kick taken by Bruno Saltor.58:57
Craig Mackail-Smith is ruled offside. Indirect free kick taken by Peter Clarke.58:25
Effort from inside the area by Lee Novak misses to the left of the target.56:00
Inswinging corner taken by Oliver Norwood.54:44
Inswinging corner taken by Daniel Ward, save made by Peter Brezovan.52:10
Adam Clayton gives away a free kick for an unfair challenge on Will Buckley. Gordon Greer restarts play with the free kick.51:07
Inswinging corner taken right-footed by Oliver Norwood, save by Peter Brezovan.47:45
Inswinging corner taken from the left by-line by Oliver Norwood.46:08
Marcos Painter is penalised for a handball. Free kick crossed left-footed by Daniel Ward from right channel, Gordon Greer makes a clearance.45:01
The second half has started.45:00 +3:06 Half time
Half Time The ref blows to signal half-time.44:40
Foul by Keith Southern on Liam Bridcutt, free kick awarded. Free kick taken by Bruno Saltor.43:45
Lewis Dunk takes the free kick.43:45 Booking
Booking The referee cautions Lee Novak for dissent.43:38
The referee penalises Lee Novak for handball.40:45
Free kick awarded for an unfair challenge on Joel Lynch by Craig Mackail-Smith. Joel Lynch restarts play with the free kick.39:39
The assist for the goal came from Craig Mackail-Smith.39:39 Goal scored
Goal! - Will Buckley - Huddersfld 0 - 2 Brighton A goal is scored by Will Buckley from deep inside the penalty box to the bottom left corner of the goal. Huddersfield 0-2 Brighton.37:07
Andrea Orlandi takes the free kick. The referee blows for offside against Ashley Barnes. Direct free kick taken by Alex Smithies.37:07 Booking
Booking Caution for Oliver Norwood.36:42
Free kick awarded for an unfair challenge on Dean Hammond by Oliver Norwood.34:27
Simon Church has a headed effort from close in and clears the bar.33:53
Corner from the right by-line taken by Daniel Ward, save by Peter Brezovan.33:19
Inswinging corner taken by Oliver Norwood.31:21
Free kick awarded for an unfair challenge on Simon Church by Liam Bridcutt. Oliver Norwood takes the direct free kick.28:18
Oliver Norwood is penalised for a handball. The ball is crossed by Andrea Orlandi, Lewis Dunk takes a shot. Alex Smithies makes a save.24:36
Long range shot from Adam Clayton misses to the left of the goal.23:05
Foul by Bruno Saltor on Daniel Ward, free kick awarded. Free kick taken by Oliver Norwood.21:42
Unfair challenge on Marcos Painter by Keith Southern results in a free kick. Peter Brezovan takes the free kick.18:52
Jack Hunt crosses the ball.16:20
Corner taken left-footed by Andrea Orlandi, Ashley Barnes produces a header from inside the area that goes over the crossbar.15:10
Ashley Barnes produces a right-footed shot from the edge of the box and misses to the right of the target.8:52
Liam Bridcutt gives away a free kick for an unfair challenge on Daniel Ward. Adam Clayton produces a strike on goal direct from the free kick, Peter Brezovan makes a save.8:17
The assistant referee flags for offside against Ashley Barnes. Free kick taken by Jack Hunt.4:34
The assist for the goal came from Bruno Saltor.4:34 Goal scored
Goal! - Will Buckley - Huddersfld 0 - 1 Brighton Will Buckley finds the net with a goal from the edge of the area high into the middle of the goal. Huddersfield 0-1 Brighton.4:00
Short corner taken by Marcos Painter from the right by-line.2:43
Effort from the edge of the penalty box by Craig Mackail-Smith goes wide of the right-hand upright.1:57
Joel Lynch challenges Will Buckley unfairly and gives away a free kick. Free kick taken by Ashley Barnes.0:00
The ref blows the whistle to start the match.
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