The Gunners gave a debut to summer signing Bacary Sagna while Danish striker Bendtner was given a chance to impress after returning from a season on loan with Birmingham City.
Sagna seemed to be a little off the pace in a first-half that was largely dominated by the French side, before Flamini struck just before the break.
The new arrival from Auxerre was caught out of position on a couple of occasion as Frau, Peguy Luyindula, and Pauleta all came close to giving Paul Le Guen's side the lead.
Arsenal, on the other hand, were struggling to get anything going, with a curled Robin Van Persie free that flew over the bar being the best they could manage.
That was until Flamini timed a perfect run into the box just before the break to latch onto a chest down from Bendtner, before confidently placing the ball home.
The French side continued to make Arsenal look ordinary in the second-half as both sides made a number of changes, but PSG's chances of clawing their way back into the match were made all the more difficult in the 68th minute when Bendtner made it two.
The Dane rose up to fairly challenge PSG keeper Mickael Landreau after a corner had been swung in, and as the ball dropped loose he reacted quickest to turn it home from close range.
The French got a goal back 10 minutes from time when some lovely build-up play down the right saw Luyindula cleverly flick home Jermey Clement's low cross from close range.
Arsenal had the chance to restore their two goal advantage just three minutes later when Alexander Hleb was brought down in the box, but Bendtner rather tamly struck the resulting penalty which was easily saved by Landreau.
However, that didn't matter as Arsenal strolled to victory, and they pick up five points (three for the win, and two for their goals) while Paris get a point for their goal.
Valencia 2-0 Internaztionale
In the day's opening game at the Emirates Stadium, Internazionale had a tough run-out as they lost 2-0 to Valencia and also watched nervously as Zlatan Ibrahimovic hobbled off in the first-half with an apparent groin injury.
In what was a far tamer affair than the "Battle of the Mestella" between the two sides in last season's Champions League, Valencia looked much sharper as they played the much crisper football in the first-half.
They took the lead in the 13th minute when Ruben Baraja picked Jamie Gavilan out at the back post with a fantastic cross field pass which the winger then fired low and under the body of Francesco Toldo into the Inter goal.
An under strength Inter side looked very sluggish in the first-half and were forced to replace Ibrahimovic with Adriano just after the half hour mark as the Swedish forward held his side in a way that suggested a groin injury.
Inter nearly levelled when Maxwell cannoned a long distance effort off the post, but then found themselves two down before the break when David Villa curled a free-kick home with the help of a deflection off Gavilan.
Both sides created a few half-chances in the second-half but a rake of substituions took the fizz out of the match.
New Inter signing Suazo looked lively up front but seemed to have left his shooting boots at home, while Miguel Angulo should have scored a third for Valencia near the end but he couldn't make contact with the ball from six yards out after it had been flashed across the box.
Valencia picked up the three points for the victory and also two bonus points as each goal scored in the competition is rewarded with an additional point.
Sunday's matches see Paris St. Germain taking on Valencia first, followed by Arsenal's clash with Inter.