The 29-year-old dispatched low into the bottom left corner in the 17th minute at St James' Park after reacting quickest on the rebound.
Almiron was first to react to Gianluigi Donnarumma's parry from an Alexander Isak's shot.
Latching onto the ball, the right winger bended a beautiful strike into the far corner as the home fans erupted into euphoria.
It is Newcastle's first Champions League goal since Alan Shearer scored in a 2-2 draw against Inter Milan at the San Siro in 2003.
Newcastle were fully deserving of their opener with PSG unable to deal with the Toon's high press.
READ MORE ON NEWCASTLE
Andy Carroll wanted to fail Liverpool medical before club-record transfer from Newcastle
Mbappe needs gloves for Newcastle cold while Luis Enrique has moment with Sir Bobby bust
Almiron has been in fine form this season, with the Paraguay international now having three goals to his name in all competitions.
Eddie Howe's side knew going into the match they had to pick up a win to boost their chances of progressing into the knockout stages.
The Premier League side held AC Milan to a 0-0 draw in Italy in their first match of Group F.
And things got even better for Newcastle and their supporters ahead of the break as they doubled their lead over the Ligue 1 champions.
Most read in Champions League
Newcastle 3-1 PSG LIVE: Boyhood Toon fans Burn and Longstaff score as hosts dominate
Lifelong Newcastle fan Dan Burn scores diving header against PSG after lengthy VAR check
Leipzig vs Man City LIVE: Reigning champions look to bounce back from consecutive defeats
Vertonghen calls for Spurs vs Liverpool Champions League final replay after Klopp comments
Versatile defender Dan Burn popped up in the 39th minute to send the home faithful into delirium.
There was a lengthy VAR check after Donnarumma attempted to claw the ball away.
But replays showed the ball crossed the line to give Newcastle a two-goal lead.