Alexander Isak had fired the Magpies ahead in the first half at the Parc des Princes after Gianluigi Donnarumma had spilled Miguel Almirón's shot.
And Eddie Howe's side looked good value for their win after turning in a terrific, determined defensive display at the home of the French champions - until Tino Livramento was harshly penalised for a handball deep into second half stoppage time.
After a VAR check, in which referee Szymon Marciniak consulted the pitchside monitor, the spot-kick was given and converted by Mbappé at the death, leaving United devastated - but still firmly in contention for qualification from Group F.
The hosts were quick out of the traps in the French capital. Lee Kang-in miscued a volley and Fabian Ruiz volleyed the loose ball over the bar as PSG fired an early warning. They could have gone ahead soon after when Mbappé backheeled Achraf Hakimi's low cross goalwards, but Nick Pope did well to react and prevent the opener with his feet.
It was then Newcastle's turn to threaten. With 12 minutes gone, the ever-lively Almirón robbing Hakimi of possession down by the corner flag. He cut the ball back perfectly for Isak and the Swede's first-time finish carried plenty of power, but flew just over the bar.
Just after the midway point in the half, though, and with United having found their feet, Howe's men moved in front. Livramento and his fast feet contributed heavily to Isak's goal; the full back's mazy dribble took him into the PSG box and his ball out to Almirón allowed the Paraguayan a sight of goal. Lewis Miley's run gave him space to shoot but his low strike was spilled by Donnarumma and Isak was there to slam home his ninth goal of the season from close range.
PSG piled some pressure on towards the end of the half, with Ousmane Dembélé testing Pope with a trickling shot the England stopper had to keep out at full stretch and then being denied by Fabian Schär's point-blank block in added time, but the Magpies' defensive discipline was helping them retain control of the contest.
Predictably, Luis Enrique's side continued to apply pressure after the restart. Randal Kolo Muani snook in and was foiled by Pope, who rushed off his line to snuff out the danger before Mbappé misconnected with his overhead kick as he looked to snaffle up the rebound.
With 25 minutes to go, Pope - who has so often produced vital stops for his side over the last season and a half - pulled off a stunning save to prevent substitute Bradley Barcola from turning home Mbappé's cutback in the six yard box. It was a magnificent and crucial intervention, throwing out his right arm to stop the shot and see it away safely for a corner.
Schär did brilliantly in the closing stages to put Dembélé off as he tried to fire home Ruiz's low cross at the near post, and Mbappé went even closer shortly after, blasting a shot straight at Pope before pulling his left-footed strike from the rebound just past the upright. Barcola then scooped a volley over the top but deep into stoppage time, the game turned on a VAR call.
Livramento was the unfortunate party, adjudged to have handled when a cross struck his torso before catching his arm. After a VAR check, referee Marciniak - who took charge of both last season's Champions League final and the 2022 World Cup final - went to the pitchside monitor and awarded a penalty, which Mbappé fired home in the 98th minute to break United's hearts in the city of love.
