Despite making 11 changes and giving senior debuts to three academy players, Palace needed just five minutes to take the lead.
Two of their more senior players on the pitch combined as Justin Devenny fed Christantus Uche, who curled beautifully into the top corner with the outside of his right foot from the edge of the box.
Romain Esse almost doubled the Eagles’ advantage when his deflected effort from an angle whizzed just wide of the post, before 16-year-old Joel Drakes-Thomas - a bright spark on his maiden appearance - struck just off target from range.
Palace also kept KuPS at bay in the first half, as the visitors recorded no shots at goal.
However, it took only five minutes of the second half for KuPS to score their first away goal of the UECL campaign, as Saku Savolainen squared for Piotr Parzyszek to finish neatly and stun the hosts.
Remarkably, Palace then found themselves behind moments later when Ibrahim Cisse poked home Clinton Antwi’s speculative strike following a corner.
The same combination for KuPS’ first goal had the ball in the net again before the hour mark, with Parzyszek tapping in Savolainen’s back-post cross, but luckily for the hosts, it was disallowed for offside.
KuPS eventually shot themselves in the foot, though, as Antwi was sent off for a horrible lunge on substitute Will Hughes.
Minutes later, another substitute, Tyrick Mitchell, crossed for Devenny to head home his first European goal and level proceedings.
Drakes-Thomas tried to inject some life from the flank later on, but his shot from the edge of the area only found Johannes Kreidl’s arms.
With the spoils ultimately shared, both Palace and KuPS must now face the play-offs, a result the latter will be happier with, having started the matchday outside the top 24.
Flashscore Man of the Match: Justin Devenny (Crystal Palace)