The victory completed another remarkable chapter in Palace's history after they also won the FA Cup and Community Shield during Glasner's time at the club. It was also the Eagles' first major European trophy and secured Europa League football for next season.
The final was a tight contest for long periods, with Rayo Vallecano enjoying more possession and controlling large spells of the game. However, Palace showed their quality when it mattered most.
The breakthrough came early in the second half after Adam Wharton tested goalkeeper Augusto Batalla with a powerful strike from distance. Batalla could only push the ball into danger and Mateta reacted quickest to fire home from close range.
Mateta's winner completed an incredible turnaround in his season after the striker had pushed for a move away from the club during the January transfer window before staying at Selhurst Park.
Palace had already missed a huge opportunity before the break when Tyrick Mitchell headed wide from close range after a superb delivery from Wharton.
After taking the lead, Palace looked dangerous and nearly doubled their advantage. Yeremy Pino struck a brilliant free-kick against both posts before Mateta hit the woodwork moments later. Batalla also produced an excellent save to deny the French striker a second goal.
Despite a late push from Rayo, Dean Henderson was rarely troubled as Palace defended strongly to protect their lead.
Glasner praised his players after the final whistle and admitted the evening was difficult to believe.
"I have to congratulate the players because this was the game we expected," Glasner told media.
"I think we played incredible football for 15 minutes after half-time. We scored the goal and could have decided the game there.
"At the end we defended so well. This group of players, this club and these fans deserve to win the Conference League."
The Austrian also reflected on his decision to leave the club after overseeing the most successful spell in Palace's history.
"I can't even believe this was the last game," he said.
"It was a great chapter in the Crystal Palace story, but more chapters will follow. The players and fans now have what they deserved after winning the FA Cup — Europa League football."
Match-winner Mateta was full of emotion after helping Palace make history.
"I feel fantastic. We did it," he said.
"It's our first time in Europe and now we just want to celebrate.
"We gave everything tonight and that's why we won."
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