The big spending French outfit ended their campaign with 11 points from six games. Liverpool, who beat Napoli 1-0 at Anfield on Tuesday night, were second with nine points.
Napoli, who also had nine points, finished third because they had scored fewer goals than Liverpool. The Italians will play in the Europa League.
That prospect faced PSG on 28 November when they hosted Liverpool at the Parc des Princes. But goals from Juan Bernat and Neymar helped them to a 2-1 victory that night.
While Bernat failed to add his name to the scoresheet at the Rajko Mitic stadium in Belgrade on Tuesday night, Neymar was again on the mark. The 26-year-old Brazilian scored just before half-time to give PSG a 2-0 lead following Edinson Cavani's opener.
Marko Gobeljic halved the deficit shortly after the pause. But the visitors restored their two goal advantage in the 56th minute when Marquinhos powered home a header.
With PSG in cruise control at 3-1 up, Kylian Mbappé added the gloss in stoppage time.
"We made mistakes but I really liked the reaction after Belgrade's goal," Tuchel told RMC Sport after the win. "We need to stay humble and have a professional attitude. We are improving and we are hard to beat."
Passage into the knockout stages as group winners will allow PSG to avoid the likes of Barcelona in Monday's draw.
"We knew qualification was going to go to the very end ever since the draw," said Marquinhos. "We knew this group was very difficult, so it's great to finish first. It's a good sign for the future."