Two goals from top scorer Chris Wood and a magnificent rearguard action saw the Clarets create a piece of Premier League history and move further away from the bottom three.
Despite a six-match unbeaten run, Burnley went into the game in the drop zone following Cardiff City’s after win at Southampton.
But Sean Dyche's men responded superbly to that potential set-back to leapfrog both the Saints and Newcastle in a congested scrap in the bottom half of the table thanks to a clinical raid on the south coast.
And Wood’s deadly double, combined with a second penalty in two games from Ashley Barnes, made it a record run without defeat in the Premier League as Burnley made it a magnificent seven.
Former Burnley loanee Shane Duffy pulled a goal back late on as Brighton tried in vain to stop the rot.
But that was the only time they found a way past an inspired Tom Heaton as the Clarets produced the kind of disciplined, determined performance that has been their hallmark in establishing a top tier place they are doing everything not to relinquish.
Cardiff last-gasp victory earlier in the day had raised the stakes for both sides and Brighton, with just one win in 10 league games, knew they would be sucked even further into the dogfight if they failed to collect three points for the first time this year.
And only the brilliance of Heaton denied the Seagulls an early goal as the Burnley - again unchanged but missing wingers Johann Berg Gudmundsson and Robbie Brady with minor knocks - were slow to get going.
The Clarets’ skipper first touched over a header from Solly March before making a flying save to keep out a volley from Pascal Gross.
But neither were a patch on the stunning stop he made to keep out another March effort which was seemingly past him before he stuck up a right hand to palm the ball away.
And 60 seconds later the Clarets were in front with 25 minutes gone.
Dyche’s men had become a growing force and Barnes should have headed them in front 15 minutes in with an effort he headed onto the bar after Duffy had deflected a cross from Dwight McNeil against the frame of the goal.
But the striker made amends with a vital contribution to a classy opening goal.
Barnes had been a big Brighton favourite during his time at the south coast, but he punished his former club with a superb touch and first-time ball in behind the Albion defence to find another ex-Seagull in Wood.
The pair had been an effective partnership for Brighton as they won promotion from League One in 2011 and their impact for Burnley continues to grow, with Wood running through to benefit from Barnes' vision and bury his eighth goal of the season and sixth in total against his former employers.
Phil Bardsley and Barnes then worked Brighton keeper Mat Ryan but in a pulsating end to the first half it took a monumental effort from the Clarets to preserve their lead.
Heaton finger-tipped the ball off the head of top scorer Glenn Murray and those in front of him also dug deep, Bardsley blocking another Gross effort and Jeff Hendrick clearing off the line from Duffy’s powerful header as Brighton were kept at bay.
The start of the second half continued in similar vein as Brighton cranked up the pressure and Burnley struggled to keep the ball long enough to stem the tide.
But they continued to defend magnificently and with just over an hour gone grabbed a second goal through the predatory Wood to double their lead.
James Tarkowski, a tower of strength alongside Ben Mee in the middle of the Clarets’ back four, played a key role with an excellent clearing header to Ashley Westwood.
Westwood helped the ball on to McNeil and a typical driving run from the teenager ended with a pass into the path of Wood, who swept a low shot first time past Ryan into the bottom corner.
And 13 minutes later it was 3-0 as the Clarets seemingly wrapped up an epic victory as they, for once, had the luck go their way in the penalty lottery.
Hendrick appeared fortunate to avoid being penalised for handball at one end before Burnley broke to get a penalty of their own when Barnes was tripped by Ryan.
For the second week running – having ended a 67-game wait for a Premier League penalty with a last-gasp leveler against Southampton a week ago – Barnes held his nerve to slot home the spot-kick.
Any thoughts the Clarets would cruise over the line were dismissed just two minutes later when Duffy finally found a way past Heaton to head home from a free-kick.
But there was no way Dyche’s men would be beaten again as they stood firm to become the first side outside the top five to win at the Amex Stadium this season and move level on points with Brighton and Crystal Palace in 13th place as their survival bid gathered further pace.
Burnley: Heaton; Bardsley, Tarkowski, Mee, Taylor; Hendrick, Westwood, Cork, McNeil; Wood, Barnes. Substitutes: Hart, Lowton, Gibson, Crouch, Ward, Vydra, Long.
Brighton: Ryan, Montoya, Duffy, Dunk, Bong; Stephens; March (Knockaert 48), Gross (Bissouma 66), Propper, Locadia (Jahanbakhsh 66); Murray. Substitutes: Button, Kayal, Bernardo, Burn.
Referee: Stuart Attwell