The Gunners started 1-0 down after being edged out at the Emirates in the first game last week.
They went into the match hoping for a comeback against the team many rate as the best in Europe at the moment – and made a strong start.
PSG keeper Gianluigi Donnarumma was forced to make some remarkable early saves to deny Gabriel Martinelli and Martin Odegaard.
Khvicha Kvaratskhelia hit the post for the hosts in the 17th minute, before Fabian Ruiz’s strike found the back of the net 11 minutes later.
It came against the run of play and left the visitors with an even more daunting task – two goals just to get level on aggregate.
Saka’s shot mid-way through the second half looked to be curling into the top corner but was also kept out by PSG’s on-form Italian keeper.
Moments later, Arsenal looked to have been dealt a killer blow when VAR showed the hand of Myles Lewis-Skelly had brushed the ball in the box.
It appeared a harsh decision, but a strange run-up and weak penalty by Vitinha was kept out by David Raya.
The reprieve lasted only a few moments for the Gunners – Thomas Partey failing to clear a loose ball and Achraf Hakimi whipping a lovely finish into the corner in the 73rd minute.
Home fans celebrated what seemed like un untouchable three-goal lead, but three minutes later Bukayo Saka put Arsenal back in it when he knocked in a cross from Leandro Trossard.
Saka then had a huge chance in the 80th minute to make it 2-2 and set up a grandstand finish but blazed the ball over from close range with the goal at his mercy.
PSG’s Parc des Princes stadium erupted at the whistle as the French side and its Qatari backers dream of an elusive first Champions League trophy.
Arsenal boss Mikel Arteta said he was proud of the way his players performed under the pressure and that opposition keeper Donnarumma was the best player and had “made a difference for them”.
Declan Rice told reporters it was “gutting” to be out “after such a dominant start” but promised the players would “keep pushing”.
PSG can now look forward to a trip to Munich for the final against Inter Milan on 31 May.
The Italian side will also be full of confidence after coming through a 7-6 two-leg classic against Barcelona on Tuesday.
