Dembele struck in the opening minutes at the Emirates Stadium and Luis Enrique’s side held on to the lead with a composed display that kept Arsenal at bay.
PSG will head into the second leg at the Parc des Princes on May 7 as favourites to reach the final against Barcelona or Inter Milan as they look to win the tournament for the first time.
But the French champions should take nothing for granted given their history of epic European collapses.
Arsenal’s first defeat in 18 home European matches was a painful blow to their own bid to win a first Champions League crown.
Mikel Arteta had labelled Arsenal’s run to the semi-finals a “beautiful story”.
The last chapter might make for frustrating reading, but they aren’t dead and buried just yet.
The Gunners had beaten holders Real Madrid 5-1 on aggregate to reach their first Champions League semi-final since losing to Manchester United in 2009.
They could not replicate the swaggering display that blew Madrid away 3-0 in the first leg, despite a frenzied atmosphere as kick-off approached.
When Arsenal’s players gathered for a pre-match huddle in the tunnel, Declan Rice implored his team-mates to give everything as he roared “if we don’t have the ball we die”.
A video message from Arteta played on the Emirates screens struck a similarly rousing chord as the Spaniard urged fans to raise the roof.
But PSG had already eliminated Premier League champions Liverpool in the last 16 and Aston Villa in the quarter-finals, after coming back from two goals down to beat Manchester City in the league phase.
Arsenal were the one English side they had failed to conquer, losing 2-0 in north London in October.
However, PSG were without the influential Dembele for disciplinary reasons on that occasion and Luis Enrique insisted his side were “more complete” seven months on.
Dembele took just four minutes to prove the point as the France star started and finished a ruthless raid.
Taking possession in the centre circle, Dembele worked the ball out to Khvicha Kvaratskhelia and he drove at Jurrien Timber with intent.
Dembele had carried on his run into the Arsenal area and Kvaratskhelia’s perfectly weighted pass picked him out for a clinical finish that went in off the far post.
Having seized the momentum, PSG went for the kill and Marquinhos rose to meet Achraf Hakimi’s cross with a header that was just too close to Arsenal goalkeeper David Raya.
Kvaratskhelia had a strong penalty appeal waved away when Timber appeared to halt the forward’s burst into area with an arm around his chest. Kvaratskhelia was undeterred, forcing Raya to save after attacking Timber again.
Dembele was proving equally hard for Arsenal to handle, his clever run and pass reaching Desire Doue for a low strike that Raya saved at full stretch.
Arsenal had been out-gunned but they should have equalised just before half-time when Myles Lewis-Skelly’s sublime pass found Gabriel Martinelli, whose shot was superbly saved by Gianluigi Donnarumma.
Arsenal thought they had drawn level two minutes into the second half when Mikel Merino headed home from Rice’s free-kick, yet their celebrations were premature as VAR disallowed the goal for offside against the Spain midfielder.
Arteta’s men had the momentum and Leandro Trossard was inches away from equalising when Rice’s pass sent him bursting into the PSG area for a shot that Donnarumma brilliantly tipped away.
Feeling the shift in the balance of power, PSG looked to take the sting out of the game by playing at a slower pace.
The tactic almost worked to perfection when Bradley Barcola sauntered through, but with just Raya to beat he dragged his shot wide of the far post.
It was a woeful miss, leaving Luis Enrique holding his head in disbelief.
The PSG coach was in the exact same stunned pose moments later when Goncalo Ramos fired against the bar from close-range. (AFP)
