After a lengthy VAR check, Burn's header was given as a goal following more disappointing defending from PSG.
Miguel Almiron had scored earlier in the contest, the first Newcastle goal in the Champions League for 20 years.
But it would have no doubt been a special moment for Burn, who worked at a local Asda aged 16, to grab the second as a lifelong Newcastle fan.
As a lad, he was a season ticket holder at St. James' Park and played for local side Blyth Spartans.
And now he is a Champions League hero for the team he loves - though he nearly saw his effort chalked off.
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Kieran Trippier sent a free-kick into the box while PSG players were furious when the ball appeared to strike Jamaal Lascelles on the arm during the phase of play.
But moments later, after testing Gianluigi Donnarumma with a near post drive, Bruno Guimaraes dinked the ball towards the far post where no one was going to beat 6ft 7ins Burn in the air.
While Donnarumma pulled off what might have been an incredible save, the ball had already crossed the line.
After a VAR check that appeared to take forever, eventually, the goal was given and it sent the home crowd further into a frenzy.
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Almiron had earlier put the hosts ahead when he tucked in a rebound shot from Alexander Isak.
Some shocking defending from Marquinhos saw him give the ball away on the edge of the box.
Isak managed a quick shot on the swivel, which was well-saved by Donnarumma.
However, none of his defenders reacted quickest as Almiron appeared like lightning to lash in the rebound on his left-foot.