The result sees Palace qualifying for the playoff round in February to reach the round of 16.
Christantus Uche's wonderful right-foot finish put the Eagles ahead before KuPS struck twice through former Charlton forward Piotr Parzyszek and Ibrahim Cisse.
However, Justin Devenny found the net for the hosts to earn a young Palace team a playoff spot. Late on, KuPS's Clinton Antwi was shown a straight red card for a foul on substitute Will Hughes.
Glasner said afterwards: “I think all four did really well. Dean (Benamar), excellent game, but after 60 minutes cramping, so we had to take him off. This was the only sub that was not planned, but we know he came back from an injury.
“I think George King played a very consistent game, good in the build-up, making no mistakes, solid in defence.
“For me, Kaden Rodney played very well in the six, so he was also good in the pressing, but also in possession. He switched the side a few times, playing good passes, and (Joel) Drakes-Thomas right at the end, he took responsibility, created a few chances by crosses, by finishes – he's just 16 and Dean is 17.
“He (Drakes-Thomas) deserved it. He didn't really train often with us, but then he did and I like his confidence. That's what I really love for young players. He has a nice personality and I like it if they take responsibility and if they do, just do, then you make a few mistakes, it's part of it. I like the way he played today.
“I think all four players showed up and played with confidence. Again, if we have one training session together, we can't expect that everything is perfect, but they showed that they are big talents.”