The match was the second leg of the Champions League play-off round, which decided which team would advance to the group stage of the competition.
The first leg ended in a 2-2 draw at Ibrox Stadium, with Abdallah Sima and Rabbi Matondo scoring for Rangers, and Ibrahim Sangare and Luuk de Jong scoring for PSV.
In the second leg, PSV dominated the game and scored five goals to thrash Rangers 5-1 and secure a 7-3 aggregate.
The first goal came in the 35th minute when Joey Veerman crossed from the right and Ismael Saibari headed in from close range.
The second goal came in the 53rd minute when Jordan Teze's cross from the left was nodded back by De Jong and Saibari tapped in his second of the night.
Rangers pulled one back in the 64th minute when James Tavernier headed in a corner from Ryan Kent.
However, PSV restored their two-goal lead in the 66th minute when Veerman's free kick was met by De Jong, who headed in his third goal of the tie.
PSV added two more goals in the final 15 minutes to complete the rout. In the 78th minute, Veerman scored with a low shot from outside the box after a neat exchange with Danilo.
In the 81st minute, Connor Goldson scored an own goal when he diverted a cross from Sam Lammers into his own net.
The match was a disastrous and humiliating defeat for Rangers, who showed little resistance and quality. Rangers were outplayed and outclassed by PSV, who showed creativity and flair and deservedly reached the Champions League group stage for the first time since 2018.