Michael Beale’s side, who drew 2-2 draw with the Dutch outfit at Ibrox last week, deservedly fell behind in the 35th minute of the return game in the Philips Stadion when Ismael Saibari headed in.
The Moroccan attacker added a second in the 53rd minute and while Gers skipper James Tavernier pulled a goal back in the 64th minute, PSV captain Luuk de Jong wasted little time in restoring the two-goal lead with a header similar to the one he scored in Glasgow.
Joey Veerman compounded Rangers’ misery when he fired in number four before hapless Gers defender Connor Goldson scored an own goal to confirm the Light Blues will drop down to the Europa League.
It was a dismal performance from Rangers who carried almost no threat until it was too late.
From the first leg, Beale drafted in midfielder John Lundstram and winger Rabbi Matondo, with Abdallah Sima and Ryan Jack dropping out.
The home side soon warmed to the task and De Jong headed a corner over the bar before Gers keeper Jack Butland beat away a Veerman drive.
In the 19th minute, home winger Johan Bakayoko floated a cross to the back post and De Jong headed wide as PSV gradually increased the pressure.
Only a fine reaction save from Butland denied Saibari from close range and there was a VAR check seconds later when Ibrahim Sangare went down in the box under a challenge from Borna Barisic.
Rangers survived but only for a few moments, until Veerman got behind Tavernier and crossed from the byline for Saibari to head past Butland from six yards.
The goal seemed to drain Rangers of real belief and they almost came unstuck again just before the break when Bakayoko’s angled drive escaped the far post.
The start to the second half was no more encouraging for the visitors.
Barisic picked up an injury just after the break and was replaced by Dujon Sterling before the Light Blues fell further behind.
Jordan Teze’s cross to the back post evaded Tavernier and De Jong knocked the ball back for Saibari to ease into the net from close range.
Saibari went looking for his hat-trick and was denied by a Butland save.
Sam Lammers and Danilo came on for Cyriel Dessers and Nicolas Raskin and there was an quick pay-off.
Lammers took a Cantwell pass and knocked it across goal for Tavernier to steer in from a couple of yards out to give the visitors an unlikely lifeline, taken away less than two minutes later when De Jong headed in a free-kick from Veerman.
A Bakayoko drive was pushed away by Butland while at the other end Matondo hit the outside of the post with a drive.
In the 78th minute Veerman fired a pass from Teze low past Butland for number four before Goldson took a pass from his keeper and knocked the ball into his own net to complete a miserable night for the Govan side, who somehow have to regroup for the Old Firm visit of Celtic on Sunday.