Sitting 11 points adrift of safety with four games remaining, only a shock win at the home of the champions would have seen Olivier Pantaloni's men live to fight another day in Ligue 1.
However, Ajaccio could not spring the surprise required in the capital, as a brace for Kylian Mbappe alongside strikes for Achraf Hakimi, Fabian Ruiz and a Mohamed Youssouf own goal condemned L'ours to their fate.
The visitors, who were only promoted back to the big time via a second-placed finish in Ligue 2 last season, were behind through Ruiz's strike with just 22 minutes on the clock, as the Spaniard created a yard of space in the box and poked home with the outside of his left foot.
Hakimi doubled PSG's lead from a tight angle in the 33rd minute after an Mbappe attempt was parried into his path, before a chaotic pinball episode in the Ajaccio box ended with Mbappe squirming a shot through the body of Francois-Joseph Sollacaro in the 47th minute.
The Frenchman doubled his tally just seven minutes later with a thunderous volley from the edge of the box, before a 73rd-minute Marquinhos strike took a significant deflection off Youssouf into the back of the net.
A mass brawl towards the end of the game saw both Hakimi - for the second time in two games - and Thomas Mangani sent off, as Ajaccio went back down to the second tier with a whimper.
Pantaloni's side, who have scored a league-low 22 goals this term, can only finish as high as 17th in the final weeks of the season, but they would need to win their last three games and hope Nantes suffer three successive defeats with a goal difference swing of at least 29.
For PSG, Christophe Galtier's side remain six points clear of Lens at the top of the Ligue 1 table and could potentially clinch the title next weekend if results go their way.