Luis Suarez broke the deadlock at Estadio Jose Alvalade on Tuesday in the 74th minute.
Khvicha Kvaratskhelia levelled just five minutes later but Suarez popped up with his second of the night on 90 minutes to seal all three points.
The result leaves both teams on 13 points, with PSG one place better off in fifth.
Luis Enrique's side had been the dominant team throughout the tie, starting with Nuno Mendes forcing Rui Silva into a sharp save early on.
And the visitors thought they had taken the lead on the half-hour mark when Warren Zaire-Emery headed in Fabian Ruiz’s cross, but the goal was ruled out by VAR for a foul in the build-up.
PSG scored again with Nuno Mendes finishing from close range after a Zaire-Emery cross, but this time an offside call against Ousmane Dembele meant that the goal chalked off.
Sporting's first shot on target then saw them open the scoring with Suarez slotting a low shot past Lucas Chevalier after Geny Catamo’s attempt rebounded into his path.
Substitute Kvaratskhelia smashed home a excellent equaliser but Suarez was well placed to steal all three points at the death.
PSG next play Newcastle United as Sporting face Athletic Bilbao.
“We had too many chances and didn’t score – it happens to us too often. We lacked concentration and made two mistakes. We do what we can, but if we don’t convert our chances, we cannot afford to concede goals,” said PSG midfielder Vitinha after the match.
Enrique added: "This result is so unfair. It's disappointing, and for me as a coach, you have to accept all possible situations in a football match, but it's incredible.
"For me, and I say this honestly as always, we played our best away match of the season. We overcame the opponent throughout, controlled the match and created lots of chances. But we’re not stupid, and we know that you have to score goals.
“I think we did everything to win this match, we were far superior, and it’s so unfair that it’s frustrating for us as a team to accept it.”
Chelsea are continuing to grapple with a virus that has disrupted preparations ahead of their upcoming Champions League fixture, with Enzo Fernandez the latest to be affected.
Arsenal secured a 3-1 victory over Inter Milan at the San Siro on Tuesday to confirm their place in the Champions League last 16 and maintain a perfect record in the league phase.
Liverpool head coach Arne Slot has played down recent tensions surrounding Mohamed Salah, insisting the matter is now firmly in the past following the forward's return to Anfield.
Manchester City's difficult run continued with a damaging 3-1 defeat away to Bodo/Glimt in Norway, compounding the disappointment of their loss to Manchester United at the weekend.
