On a tough night for the Light Blues, who will now go into Friday’s Europa League group stage draw, a header from Ismael Saibari on 35 minutes put the Eredivisie club in front and the impressive number 34 made it 2-0 on 53 minutes.
James Tavernier pulled one back after the hour mark but PSV quickly restored their two-goal lead, with Luuk De Jong heading past Jack Butland from a free-kick. A low strike from Joey Veerman and an own goal from Connor Goldson completed the second-half scoring.
Prior to kick-off an impressive light show helped to build up the pre-match atmosphere, with the stadium packed in anticipation.
With Jose Cifuentes returning to the starting eleven on the right side of a compact four-man midfield, and Rabbi Matondo also back in the team on the left, the shape of the Rangers team was certainly different to the first leg at Ibrox.
And the Light Blues enjoyed a positive start to this contest with Tavernier chipping the ball cleverly over the PSV defence to Cifuentes who powered a low, dangerous delivery into the box but there were no takers.
It was good play from the Gers but the home side gradually worked their way into the match, with captain and main striker De Jong given too much space to head over from a Veerman corner with nine minutes on the clock.
Veerman then tried his luck from distance, the creative midfielder’s shot stinging Butland’s hands as the goalkeeper pushed the ball to safety.
Before the 20-minute mark PSV should have got their noses in front when Johan Bakayoko’s curling back-post cross from the right wing was met by De Jong who, from just a few yards out, headed wide of Butland’s right-hand post.
With half an hour played the game remained goalless but Rangers had their in-form number one to thank for keeping it that way. An excellent cross from the left found Saibari but his first-time shot brought out an excellent save the Gers goalie with his legs.
The pressure was building and on 35 minutes it was Saibari who broke the deadlock. Again a cross came in from the left, this time from Veerman, and the Spanish-born Moroccan international rose above the defence to accurately head the ball into the net.
On chances created and goal attempts, Bosz’s men deserved to be in front at the half-time break but, with just one goal separating the sides at this point, Rangers had an opportunity to regroup.
PSV, however, were putting in a ruthless performance in front of their vociferous support and, with the Light Blues losing left-back Borna Barisic through injury at the start of the second period, it was Saibari who doubled his side’s advantage on 53 minutes.
Jordan Teze dinked a deep cross for Noa Lang who crossed on the volley to his teammate who did well to control a first-time finish.
Rangers tried to find a way back into the game, with a glancing header from Goldson from Tavernier’s cross going inches wide of the far post.
But PSV continued to pile drive forward with power and pace, and Saibari again brought out a terrific save from Butland after he jinked past several Rangers players before trying his luck from 20 yards with a low drive.
With the visitors in need of a spark in the final third, Danilo and Sam Lammers went on with 61 minutes played and four minutes later Michael Beale’s men pulled a goal back.
Todd Cantwell dinked a ball over the PSV backline to Lammers who crossed to the back post and Tavernier was there, as he so often does, to fire the ball high into the net.
But just when it looked like Rangers were going to ask questions of the home team, two minutes after scoring they conceded a third goal, with De Jong heading past Butland from Lang’s free-kick.
Lammers had an impact going on, the Dutch forward providing the assist for Tavernier’s goal and, on 73 minutes, he cut inside and hit a left-foot shot which Walter Benitez watched closely as it flew wide of target.
Matondo then used his pace and skill to find a path into PSV’s 18-yard box and he clattered the post with an impressive individual effort.
The home side, however, were more decisive and dangerous in the final third and on 78 minutes they added a fourth goal.
Bakayoko found Teze overlapping and his cut-back cross was perfect for Veerman who took one touch before he arrowed an accurate finish across Butland and into the far bottom corner.
With nine minutes remaining it was 5-1, with Goldson scoring an uncharacteristic own goal. Butland passed the ball to the centre-half who then put too much on his return pass and the ball rolled painfully beyond the Gers goalkeeper and into the net.
PSV: Benitez, Teze (Sambo 83), Sangare, Lang (Ramalho 68), Dest, De Jong, Bakayoko (Tillman 87), Boscagli (Til 83), Schouten, Veerman, Saibari (Vertessen 87)
SUBS NOT USED: Drommel, Waterman, Pepi, El Ghazi, Babadi, Van Aanholt
GOALS: Saibari 35, 53, De Jong 66, Veerman 78, Goldson 81og
RANGERS: Butland, Tavernier, Goldson, Souttar, Barisic (Sterling 51), Cifuentes, Lundstram, Raskin (Lammers 51), Matondo (Jack 85), Cantwell, Dessers (Danilo 51)
SUBS NOT USED: McCrorie, K. Wright, Sima, S. Wright, Davies, Balogun, King, Devine
GOALS: Tavernier 64
BOOKINGS: Matondo
REF: Jose Maria Sanchez (ESP)