A win for Arsene Wenger's side would have ensured that they would take their place among the seeds when the draw for the knockout stages is made next month, but a late own goal from Alex Iwobi left the Premier League side facing the prospect of finishing as runners-up.
Arsenal can still finish in first spot should they beat Basel in Switzerland and PSG slip up against Ludogorets, but they are likely to face tough opposition when they find out who awaits them in the last 16.
During the second half against Manchester United on Saturday afternoon, Arsenal scored with their only shot on goal and history repeated itself during the opening 45 minutes on Wednesday night.
Paris Saint-Germain were not exactly relentless in their bid to create opportunities in North London but minutes after Thiago Silva had seen an effort cleared off the line by Kieran Gibbs, they got themselves in front.
It was a goal which should have led to a response from the home team but they toiled against the French champions and it was PSG's own doing that they did not reach half time with a one-goal advantage.
After Gregorz Krychowiak had brought down Alexis Sanchez in the penalty area, Olivier Giroud stepped up to fire his spot kick into the corner to get his team back on level terms against the run of play.
The same pattern of play continued after the restart before PSG came agonisingly close to retaking the lead when Lucas Moura's 25-yard free kick hit the crossbar with Ospina beaten.
That near miss was soon followed by Arsenal taking the lead in the most fortuitous circumstances as Aaron Ramsey's shot was blocked by Silva before the ball ricocheted off Marco Verratti and headed into the bottom corner from 10 yards out.
For the following 15 minutes, the Gunners did an effective job in stifling the visitors but as the game entered the closing stages, PSG found an equaliser when Moura's header was deflected into his own net by Iwobi.
In the space of a couple of minutes, Moura created two opportunities for Cavani but after squandering a one-on-one chance under no pressure, the Uruguayan glanced a header wide of the post when it looked easier to score.
However, as Arsenal tired during the closing stages, it mattered little as PSG comfortably held on to leave their fate in their own hands when they face Ludogorets in Paris in two weeks' time.