The Gunners needed just a point to qualify for the last-16 with a game to spare, but second-half goals from Joey Veerman and Luuk de Jong put the North London club to the sword as their perfect European record came to an end.
Straight off the bat, PSV looked a totally different side from the one that was nullified at the Emirates last week, in spite of Mikel Arteta opting for a strong first XI.
Cody Gakpo and Xavi Simons sought to terrorize the Arsenal defence, and both attackers had the ball in the back of the net for PSV, but the offside flag saved Arsenal's bacon.
The high line of Arsenal caught out Gakpo before he chipped the ball over the onrushing Aaron Ramsdale - making his European debut - before Simons had seemingly given PSV the lead on the stroke of half time.
However, a VAR review led to the goal being ruled out for offside on Anwar El Ghazi, but the Arsenal defending was certainly questionable as Simons evaded a sea of black shirts before slotting home from close range.
In contrast, Arsenal produced a rather tepid attacking performance in the first half, with Martin Odegaard stinging the palms of Walter Benitez and Gabriel Martinelli firing an acrobatic effort over the top in their best two chances of the opening 45.
Despite a couple of half-chances for Arsenal early in the second 45, PSV would have the ball in the back of the net for a third time in the 55th minute, and this one would count, as De Jong held off the challenge of Rob Holding and laid off Veerman to finish clinically into the top corner.
It was no less than Ruud van Nistelrooy's side deserved, and their lead was doubled just after the hour mark, as Ramsdale came out to meet a corner but failed miserably, allowing De Jong to head home into an empty net.
Gakpo soon had another goal ruled out for offside as Arsenal tried and failed to find answers, and it took until the 79th minute for the Gunners to have a shot on target in the second half, as Benitez kept out Eddie Nketiah's point-blank effort before Everton loanee Jarrad Branthwaite made a vital last-ditch challenge.
Late Arsenal pressure was comfortably quelled by PSV, and the Gunners need a win against FC Zurich at home next week to make sure of a place in the last-16, while PSV have cut the gap down to two points before they tackle Bodo/Glimt next week.