First-half goals from Kai Havertz and Bukayo Saka helped the Gunners on their way, as Mikel Arteta's men record their first win of the new Champions League campaign.
Set-pieces proved vital once again in what was a close encounter with few chances created by either team, as both Arsenal goals came from crosses from out wide.
Leandro Trossard delivered a sumptuous cross for Havertz's opener on 20 minutes, but it was Donnarumma's error which made the chance easier for the German, racing out and getting nowhere near the ball.
All eyes were on PSG's number one again 15 minutes later, as Saka's free kick flashed through everyone in the area, and past him down the middle of the goal as Arsenal added a second shortly before the interval.
Both of PSG's full-backs, Achraf Hakimi and Nuno Mendes, went close in the opening period, with the latter grazing the woodwork, but despite having the lion's share of possession, the visitors struggled to get themselves back in the game.
Gabriel Martinelli should have put the game beyond PSG early in the second half, but fired straight at Donnarumma when presented with an opportunity one-on-one, and that inability to get a third goal left them exposed to a comeback, and Joao Neves hit the bar from a corner midway through the second half.
With one of the finest defences in Europe though, Arsenal dealt with the PSG threat comfortably to keep another clean sheet, meaning Luis Enrique's side have still only scored once in the UCL this season - a late own goal against Girona.
ARSENAL VS. PSG HIGHLIGHTS
Havertz goal vs. PSG (20th min, Arsenal 1-0 PSG)
A devilish cross from Trossard dropped in behind the PSG backline forces Donnarumma to race off his line, but the Italian is caught in no man's land and is beaten to the ball by an on-rushing Havertz, who heads into the vacant goal to give Arsenal the lead!
Saka goal vs. PSG (35th min, Arsenal 2-0 PSG)
Saka whips in a low left-footed, right-wing cross, which evades everyone in the area, including goalkeeper Donnarumma, who sees the ball sail past him and into the back of the net directly from the free kick.
MAN OF THE MATCH - KAI HAVERTZ
As well as getting the opening goal of the evening, Havertz excelled at implementing Arsenal's high press which gave the PSG backline a torrid night, and the German once more showed why talk of the Gunners needing to sign a central striker have died down.
ARSENAL VS. PSG MATCH STATS
Possession: Arsenal 39%-61% PSG
Shots: Arsenal 7-10 PSG
Shots on target: Arsenal 4-3 PSG
Corners: Arsenal 1-4 PSG
Fouls: Arsenal 5-8 PSG
BEST STATS
WHAT NEXT?
Arsenal will be heavy favourites to keep their unbeaten start going when they welcome Southampton to the Emirates on Saturday, while PSG face a relatively difficult trip down south to face a rejuvenated Nice side.