Roared on under the St. James' Park lights by a charged up home support, the Magpies - unchanged from the weekend's 2-2 draw at Leeds - flew straight out of the blocks, pressing the visitors high up the pitch as Roberto De Zerbi's side steadfastly attempted to play out from the back throughout the first half.
Inside the opening ten minutes, Miguel Almirón had seen a low shot deflect behind off the heel of Jan Paul van Hecke, Alexander Isak had been denied by the legs of Jason Steele and Fabian Schär had seen a long-range free kick gathered by the Seagulls' Newton Aycliffe-born goalkeeper.
Then Joe Willock stabbed wide from an Almirón cutback, before the same two players combined for another opportunity with Willock backheeling the ball into Almirón's path, but the Paraguayan curled his shot off target.
A Danny Welbeck effort from 22 yards - comfortably held by Pope - in the 16th minute was Brighton's first effort of note, but Newcastle were soon back on the attack when Joelinton's strike was blocked by Lewis Dunk.
From the resulting corner, swung in from the left by Kieran Trippier, Deniz Undav could only divert the ball beyond his own goalkeeper as he attempted to deal with a dangerous delivery from the United skipper, who was nominated for the Premier League's EA Sports Player of the Year award ahead of the game.
The noise levels increased by a few more decibels with that - and then again when Callum Wilson went down under a challenge in the box from Dunk, leading VAR Jarred Gillett to take a closer look, but he decided against recommending referee Robert Jones to take a look at the monitor.
In the 32nd minute, a low cross from Schär fizzed agonisingly across goal, then two minutes later Dan Burn, still up from a corner which had not been fully cleared, spun cleverly in the box but his left-footed shot went the wrong side of the post.
But the Blyth-born defender was on target in first-half stoppage time, rising highest to connect with Trippier's free kick. Many players opt not to celebrate scoring against a former club, but Burn certainly did - and why not, after netting his first Premier League goal for his boyhood club in such a vital match?
It should have been 3-0 early in the second half, with Burn involved again, digging out a cross from the left which Willock nodded into the path of Almirón, but Steele denied him with an excellent close-range save.
And almost immediately, Brighton pulled one back, with Undav, just onside, racing onto Billy Gilmour's pass to slot past Pope and give his side hope of mounting a comeback.
United suffered another blow when Willock pulled up inside his own half with an injury which led to him being replaced by Elliot Anderson and could well mean the former Arsenal midfielder misses the final two matches of the campaign.
Steele made another stunning save, this time from Isak's header, in the 65th minute - but the home supporters were convinced Newcastle should have been awarded a penalty in the build-up when Burn's shirt looked to be tugged by Van Hecke just inside the area.
Julio Enciso headed wide for the Seagulls and Guimarães fired narrowly over for United - but in the 89th minute, Almiron burst past Moisés Caicedo in his own half and found Wilson, who ran through to slot home his 18th goal of the season.
And in stoppage time, following unselfish play from Wilson, Guimarães made it four for Newcastle, who now know that if they can beat struggling Leicester at St. James' Park on Monday night, they will be certain of a top four finish.
