Sporting went ahead through Suarez against the run of play in the second half, despite sustained pressure from PSG.
The French champions hit back quickly as Khvicha Kvaratskhelia levelled with a superb strike, appearing to salvage a point.
Suarez, however, struck again in the dying moments to snatch victory for Sporting, leaving both teams on 13 points and inside the top eight, which assures direct qualification for the last 16, ahead of PSG’s home match against Newcastle United and Sporting’s trip to Athletic Bilbao.
Both teams lead ninth-placed Inter by a single point.
“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.
Luis Enrique’s side dominated the opening stages in Lisbon, with Nuno Mendes forcing Rui Silva into a sharp save from a tight angle and Senny Mayulu heading tamely at the Sporting goalkeeper after good work down the left.
The visitors thought they had taken the lead on the half-hour when Warren Zaire-Emery headed in Fabian Ruiz’s cross, but the goal was ruled out after a VAR review judged Mayulu had fouled Geny Catamo in the build-up.
Nuno Mendes then had the ball in the net again late in the half, finishing from close range after a Zaire-Emery cross, only for the effort to be disallowed for an offside against Ousmane Dembele.
Sporting offered little in response before the break, but the teams went in level at 0–0 despite PSG’s clear superiority with 15 attempts and 69% possession.
Sporting offered more early in the second half, with a dangerous Trincao cross just evading Suarez in the 52nd minute.
The hosts then had their first shots on target and opened the scoring in the 74th minute when Suarez coolly slotted a low shot past Lucas Chevalier after Catamo’s attempt had been deflected into his path.
Five minutes later, Kvaratskhelia, who had come on for Mayulu, unleashed a superb shot into the far top corner from the edge of the box to equalise.
But PSG lacked their usual grit and were punished again in the 90th minute.
Trincao collected a low pass from the left just outside the box and struck first time with his left foot, forcing Chevalier to parry and Suarez nodded the rebound into the far corner to send the crowd into raptures.