The Gunners had already won Group B and manager Mikel Arteta made eight changes from the weekend’s Premier League loss at Aston Villa.
Nketiah fired Arsenal ahead three minutes before the end of a first half in which they had been put under significant pressure by PSV, who had also already qualified for the knockout stages as group runners-up.
It was a superb finish by the England forward, controlling a low ball from the right before striking into the bottom-right corner from the edge of the area.
But Arsenal were pegged back five minutes after the break through Vertessen’s right-footed strike off the left post.
Arsenal conclude the group stage with 13 points from six games – four ahead of PSV – and will face one of the other seven runners-up in the next round.