Nine-man Rangers were dumped out of the Champions League by Malmo in a bad-tempered encounter in Sweden.
Nikica Jelavic's goal had levelled the tie in the 23rd minute, but red cards for Steven Whittaker and Madjid Bougherra hit Ally McCoist's side.
The Swedes were reduced to 10 men when Ferreira Ricardinho saw red, but an 80th minute goal from Jiloan Hamad put the tie out of reach.
Rangers now drop into the final round of Europa League qualifying.
Uefa sanctions meant McCoist's side were without their own supporters for the away tie in Sweden, but the Ibrox side started brightly, with Jelavic threatening in front of goal as early as the eighth minute, his run brought to an abrupt halt by Malmo keeper Dusan Melicharek.
At the other end Malmo too had early chances with Pontus Jansson blasting over the crossbar, before a dipping free-kick from Wilton Figueiredo from 22 yards out caused more of a scare, with Allan McGregor having to tip over the bar.
Rangers' task was made more difficult when Whittaker was shown a straight red card after 18 minutes when he threw the ball at Malmo midfielder Jimmy Durmaz's head during a stoppage in play.
But having lost a man, Rangers gained a goal just five minutes later, Jelavic this time connecting beautifully with Maurice Edu's cross, volleying with his right foot back across goal to level the aggregate score at 1-1.
With the tie wide open, the drama continued on and off the ball.
Lee McCulloch could have little complaint about his yellow card for a challenge on Durmaz, but the Swede escaped any kind of caution when he appeared to kick out at the Rangers midfieler while on the ground in the aftermath of that foul.
The Russian referee Vladislav Bezborodov waved away the protestations of the Rangers players on the pitch, while McCoist voiced his disapproval from the sidelines.
The controversy was to continue into the second half. The Swedish champions, seemingly buoyed by their numerical advantage, started brightly and slowly built the pressure towards the hour-mark, winning a series of corners but being unable to penetrate McGregor's goal.
With the tension building, Bougherra was the next to see red in the 66th minute, the Algerian appearing to elbow Malmo's Dardan Rexhepi on the back of the head when the two players went up for a high ball.
Reduced in number yet again, Rangers tried to hold on for extra time, but to no avail.
With 10 minutes remaining, Hamad secured a place in the final qualifying round for the Swedes, striking a controlled left-footed volley from distance which caught McGregor - who had an otherwise faultless performance - off-guard.
There were chances for Rangers in the dying minutes, including an opportunity for Steven Naismith in the final seconds which he sent over the bar, but the Swedes held on to their advantage, leaving the Scots to await their fate in the draw for Europa League fourth round play-offs.
Full Time The final whistle goes and the game is over.
Dusan Melicharek takes the free kick.
90:00 +3:21 Booking
Booking Sasa Papac receives a caution.
The referee penalises Sasa Papac for handball.
Foul by Steven Davis on Jeffrey Aubynn, free kick awarded. Free kick taken by Dusan Melicharek.
Effort on goal by Steven Naismith from just inside the penalty box goes harmlessly over the target.
Jiloan Hamad takes a shot. Save by Allan McGregor.
Effort from deep inside the area by Jimmy Durmaz misses to the left of the target.
Substitution Palazon Juanma Ortiz leaves the field to be replaced by Kane Hemmings.
79:30 Goal scored
Goal! - Jiloan Hamad - Malmo 1 - 1 Rangers Jiloan Hamad finds the net with a goal from inside the area to the top left corner of the goal. Malmo FF 1 (2)-(1) 1 Rangers.
Wilton Figueiredo takes a shot. Allan McGregor makes a save. Inswinging corner taken right-footed by Wilton Figueiredo from the left by-line, Pontus Jansson takes a shot. Save by Allan McGregor.
Jimmy Durmaz sends in a cross, Palazon Juanma Ortiz manages to make a clearance.
The referee blows for offside. Dusan Melicharek takes the free kick. Short corner worked by Wilton Figueiredo.
Unfair challenge on Steven Naismith by Jimmy Durmaz results in a free kick. Allan McGregor restarts play with the free kick. Wilton Figueiredo produces a right-footed shot from inside the area that clears the crossbar.
Nikica Jelavic has an effort at goal from just outside the penalty box which goes wide of the left-hand post.
Steven Davis crosses the ball in from the free kick, Daniel Andersson makes a clearance.
Dismissal The referee sends off Ferreira Ricardinho for second bookable offence.
Nikica Jelavic fouled by Ferreira Ricardinho, the ref awards a free kick.
Wilton Figueiredo crosses the ball in from the free kick, Palazon Juanma Ortiz manages to make a clearance.
Substitution Jeffrey Aubynn joins the action as a substitute, replacing Dardan Rexhepi.
Dismissal The referee shows Madjid Bougherra a red card for serious foul play.
Free kick awarded for a foul by Madjid Bougherra on Dardan Rexhepi.
Free kick taken by Dusan Melicharek.
Booking Steven Naismith booked for unsporting behaviour.
Free kick awarded for a foul by Steven Naismith on Jimmy Durmaz.
Nikica Jelavic is caught offside. Ferreira Ricardinho takes the indirect free kick.
Wilton Figueiredo takes a outswinging corner to the near post. Effort on goal by Filip Stenstrom from just outside the penalty area goes harmlessly over the target.
Outswinging corner taken right-footed by Wilton Figueiredo from the right by-line, clearance made by Madjid Bougherra.
Corner taken by Wilton Figueiredo, Ivo Pekalski takes has a header from just inside the penalty box which clears the crossbar.
Inswinging corner taken left-footed by Lee Wallace from the right by-line, Madjid Bougherra takes a shot. Filip Stenstrom gets a block in.
Wilton Figueiredo is adjudged to have handled the ball. Free kick crossed by Lee Wallace.
Dardan Rexhepi takes a shot from deep inside the box clearing the bar.
Steven Davis takes the inswinging corner, clearance by Daniel Andersson.
Free kick awarded for an unfair challenge on Nikica Jelavic by Daniel Andersson. Free kick crossed right-footed by Steven Davis, Ferreira Ricardinho manages to make a clearance.
Inswinging corner taken right-footed by Wilton Figueiredo, Foul by Dardan Rexhepi on Lee Wallace, free kick awarded. Allan McGregor takes the free kick.
The referee starts the second half.
Substitution Dardan Rexhepi is brought on as a substitute for Miljan Mutavdzic.
45:00 +1:38 Half time
Half Time The referee calls an end to the first half.
Free kick taken by Ivo Pekalski.
Booking Lee McCulloch goes into the referee's book.
Booking The referee cautions Pontus Jansson for unsporting behaviour.
Jimmy Durmaz fouled by Lee McCulloch, the ref awards a free kick.
Wilton Figueiredo takes the outswinging corner, clearance made by Madjid Bougherra.
Foul by Lee McCulloch on Daniel Larsson, free kick awarded. Ivo Pekalski takes the free kick.
Palazon Juanma Ortiz restarts play with the free kick.
Booking Caution for Ferreira Ricardinho.
Ferreira Ricardinho challenges Steven Davis unfairly and gives away a free kick.
Daniel Larsson is ruled offside. Allan McGregor takes the free kick.
Wilton Figueiredo crosses the ball in from the free kick, Madjid Bougherra manages to make a clearance.
Booking Maurice Edu is shown a yellow card.
Maurice Edu concedes a free kick for a foul on Jimmy Durmaz.
Nikica Jelavic gives away a free kick for an unfair challenge on Filip Stenstrom. Filip Stenstrom restarts play with the free kick.
Ferreira Ricardinho delivers the ball, Sasa Papac manages to make a clearance.
The ball is delivered by Jimmy Durmaz, Madjid Bougherra makes a clearance.
Outswinging corner taken from the right by-line by Wilton Figueiredo.
The ball is swung over by Filip Stenstrom.
Substitution Filip Stenstrom joins the action as a substitute, replacing Agon Mehmeti.
The ball is sent over by Maurice Edu, Nikica Jelavic takes a shot. Save by Dusan Melicharek.
Ivo Pekalski gives away a free kick for an unfair challenge on Nikica Jelavic. Free kick taken by Allan McGregor.
The assist for the goal came from Maurice Edu.
22:43 Goal scored
Goal! - Nikica Jelavic - Malmo 0 - 1 Rangers Nikica Jelavic scores a goal from deep inside the penalty box low into the middle of the goal. Malmo FF 0 (1)-(1) 1 Rangers.
The ball is swung over by Maurice Edu,
Jiloan Hamad concedes a free kick for a foul on Steven Davis. Strike on goal comes in from Nikica Jelavic from the free kick, Daniel Larsson gets a block in.
The free kick is delivered right-footed by Wilton Figueiredo from right channel, Palazon Juanma Ortiz makes a clearance. Effort on goal by Jiloan Hamad from just outside the penalty area goes harmlessly over the target.
Dismissal Steven Whittaker shown a red card for serious foul play.
Foul by Steven Whittaker on Daniel Larsson, free kick awarded.
Corner from the left by-line taken by Wilton Figueiredo, clearance made by Sasa Papac.
Foul by Madjid Bougherra on Agon Mehmeti, free kick awarded. Wilton Figueiredo has an effort direct from the free kick, save made by Allan McGregor.
A cross is delivered by Daniel Larsson, blocked by Madjid Bougherra.
Effort on goal by Pontus Jansson from just inside the area clears the bar.
Lee McCulloch challenges Wilton Figueiredo unfairly and gives away a free kick. The free kick is delivered right-footed by Wilton Figueiredo from right channel, Madjid Bougherra manages to make a clearance.
Inswinging corner taken by Steven Davis, Nikica Jelavic takes a shot. Dusan Melicharek makes a save. Corner taken right-footed by Lee Wallace from the right by-line, clearance by Ferreira Ricardinho.
Free kick awarded for a foul by Nikica Jelavic on Ferreira Ricardinho. Jimmy Durmaz takes the free kick. Corner taken right-footed by Steven Davis, clearance by Ivo Pekalski.
Lee Wallace produces a cross.
The referee blows for offside. Madjid Bougherra takes the free kick.
The referee blows for offside against Nikica Jelavic. Dusan Melicharek takes the free kick.
Nikica Jelavic concedes a free kick for a foul on Ferreira Ricardinho. Direct free kick taken by Daniel Andersson.
Dusan Melicharek takes the indirect free kick. Maurice Edu is ruled offside.
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