Local hero Burn gave Newcastle a deserved lead in the 45th minute of Sunday's final when the defender thumped in a header from a corner.
Roared on by a sea of fans clad in black-and-white in the 88,513 crowd, Newcastle took complete control of the match seven minutes after the break when Swedish forward Isak swept a shot past Liverpool keeper Caoimhin Kelleher.
Runaway Premier League leaders Liverpool finally mustered a response when Federico Chiesa halved the deficit in stoppage time, but the damage was done and the day belonged to Eddie Howe's Newcastle, who won the club's first domestic trophy since 1955.
Newcastle suffered heartbreak two years ago in the League Cup final against Manchester United, their ninth straight loss at Wembley, but were determined to write their names into folklore as they tapped into the energy from their supporters.
"It's all for these fans," Newcastle captain Bruno Guimaraes, who arrived at the club after the 2021 Saudi Arabia-backed takeover, said before raising the trophy aloft.
"They deserve everything. When I first came here I said I wanted to put my name in history. We can now say we are the champions again."
Liverpool on the other hand looked flat and appeared to be suffering a Champions League hangover after being knocked out of Europe by Paris St Germain on penalties on Tuesday.
One statistic summed up the Reds' day, with talisman Mohamed Salah, for the first time in his Liverpool career, having neither a shot nor creating a chance in a match in which he played 90 minutes.
Barring a collapse, Liverpool will surely win the Premier League, but manager Arne Slot's first Wembley final will not be one the Dutchman remembers fondly.
"A disappointing result and disappointing performance," he said. "The game went exactly how (Newcastle) wanted it to go. They deserved to win."
Newcastle looked the greater threat in a cagey opening half and Sandro Tonali flashed a shot past the post.
Liverpool seemed intent on reaching halftime all square and looked like achieving that modest ambition until Burn, given a first England call-up last week, sent Newcastle's fans wild.
The towering centre back was marked by the diminutive Alexis Mac Allister for Kieran Trippier's corner and it was a no-contest as he planted an unstoppable header beyond the diving Kelleher.
It was Burn's first goal of the season and Newcastle's first at Wembley for 25 years since Rob Lee scored in a losing FA Cup semi-final against Chelsea.
They did not have to wait long for their next goal, and this time it came from a more likely source.
Seven minutes after the break Jacob Murphy headed a cross into the path of the Swede who, quick as a flash, swept a shot past Kelleher in front of the massed ranks of black and white. Isak has now scored 23 goals this season.
After such a long wait it was never going to be drama-free for Newcastle's fans, most of whom were not even born when they beat Manchester City in the 1955 FA Cup final.
Chiesa's neat goal, allowed by VAR after initially being ruled offside, ensured a few thousand fingernails were chewed through stoppage time, but the final whistle ended decades of despair and triggered Geordie celebrations in the capital.
