Palace started brightly, and Ismaila Sarr nearly earned a golden chance for himself when he brought the ball down delightfully in the box, but a good block took all the pace off his effort.
Daichi Kamada then looked to be breaking clear of the defence, until Pathé Ciss scythed him down, escaping with just a yellow card.
Rayo did muster one or two warning signs of their own, Alexandre Alemao and Unai Lopez both steering efforts narrowly wide, but Tyrick Mitchell spurned the best chance on the brink of half-time when he headed a glorious Adam Wharton cross just beyond the post.
Nevertheless, the half ended without either side registering a shot on target, the note of caution perhaps understandable given that both teams were featuring in their first-ever European final.
The Eagles looked to up the tempo after the restart, and Florian Lejeune needed to be alert to stop Jean-Philippe Mateta from netting a tap-in, sliding in to cut out the delivery.
But the Frenchman was not to be denied moments later, gobbling up the rebound from close range after Augusto Batalla could only parry Wharton’s effort from the edge of the box.
Glasner’s side kept on coming, and only the finest of margins prevented Yéremy Pino from doubling the lead, with his free kick bouncing off both posts, before a combination of the woodwork (again) and the offside flag prevented anyone from smuggling in the rebound.
Mateta was then denied by a fine save from Batalla, somewhat atoning for his earlier spill, and Sarr subsequently couldn’t test the goalkeeper from close range.
Nerves started to kick in for the English outfit as the match approached its final 10 minutes, and they had to weather a few scares, but some stout rearguard action secured a special achievement.
Glasner will now depart Crystal Palace on the highest of highs, delivering the club’s finest hour in his final game in charge.
For Rayo, the nine-game unbeaten streak (W6, D3) could not have ended at a worse time, although they will still look back on a season for the ages in just their second-ever European campaign, following a run to the UEFA Cup quarter-finals in 2000/01.