Will Buckley’s brace inspired Albion to a 2-1 win over Huddersfield Town and extended the Seagulls' unbeaten run to five games.
Poyet’s side went ahead thanks to the winger’s fifth minute strike before he added a brilliant second just before half-time. Simon Church scored a late goal for the hosts but they were unable to complete the comeback.
The result saw Albion leapfrog the Terriers on goal difference but the day belonged to the magnificent Buckley.
Preparations were interrupted late on as Tomasz Kuszczak pulled up with an injury in the warm-up, so Peter Brezovan deputised for the Polish international.
The late change did not hinder Albion who were fast out the blocks, and almost went ahead within three minutes as Andrea Orlandi squared the ball back to Craig Mackail-Smith whose first-time effort went narrowly wide.
Just two minutes later though, Poyet’s side did take the lead with Buckley collecting Bruno’s pass just inside the Huddersfield box. The in-form winger’s first touch created him space before sneaking a left footed strike inside Alex Smithies' near post.
Brighton searched for a quick second and Ashley Barnes smashed the ball just wide of the Terriers' right upright.
Albion nearly extended their lead when they capitalised on referee Simon Hooper’s decision to overturn his linesman and awarded Albion a throw on the left.
Marcos Painter’s quick thinking released Orlandi down the wing before the Spaniard looped the ball into the area for Mackail-Smith to attempt a diving header. Paul Dixon just did enough to put the Albion striker off but the ball eventually reached Buckley at the far post who saw his low drive cleared off the line by Joel Lynch.
Hooper further infuriated the home fans when he waved away penalty appeals after Lewis Dunk and Peter Clarke tangled in the Brighton box, before Church spurned a glorious chance to pull the hosts level. The striker rose unmarked and headed Danny Ward’s magnificent cross from the right over from six yards.
Poyet’s men thought they had grabbed a second when Orlandi’s in-swinging free-kick from the right went all the way through and into Smithies’net, but the linesmen raised his flag for offside against Barnes, who had got the faintest of touches to help guide the ball in.
Albion were celebrating two minutes later though as Buckley doubled his tally. Mackail-Smith played the winger through the middle and he jinked his way past Clarke before drilling the ball home.
Huddersfield begun the second half with more purpose and tried to force a way back in to the game. Lee Novak was just inches from halving the deficit on the hour mark when Jack Hunt’s driven ball across the Albion box was stabbed just wide by the striker.
Smithies denied Buckley his hat-trick as the midfielder tried to curl the ball home from the edge of the area but the Terriers' keeper got down well to his right to parry the ball away.
The hosts finally broke through Albion’s resilient defence in the 90th minute to set up a nerve-racking finale when Brezovan spilled Ward’s shot and Church was on hand to tap in.
But it was Albion who nearly found a stoppage time goal when substitute Will Hoskins chipped the ball over the top for Buckley to run on to. Smithies once again denied the winger with a great save with his legs, and it proved to be the last major action as Albion held on to secure a hard-earned three points.