Rangers were sent crashing out of the Champions League after Dynamo Kyiv scored twice within two minutes in the closing stages at Hampden Park following the dismissal of home winger Jefte.
Clinical strikes from Oleksandr Pikhalyonok and fellow substitute Nazar Voloshyn mean Rangers drop into the less lucrative Europa League for the second season running.
The Ukrainian visitors head for the Champions League play-off round for the second time in three seasons and will face Salzburg after the Austrian Bundesliga runners-up overcame Twente 5-4 on aggregate following a thrilling 3-3 draw in Enschede.
But, with Rangers and Kyiv level after the first leg in Lublin, the tie in Glasgow swung on the decision to show Jefte a second yellow card five minutes after the break following an aerial challenge on Oleksandr Karavayev.
Rangers started on the front foot, with the Dynamo defence looking nervous and hesitant.
Jefte made a lively start, heading wide at the back post from a James Tavernier cross before Cyriel Dessers nodded straight at goalkeeper Heorhiy Bushchan.
Bushchan had to get down quickly to push away a low Ross McCausland strike, while Dynamo were restricted to a couple of dangerous Vladyslav Kabayev crosses flashed across the Rangers six-yard box.
Rangers manager Philippe Clement decided to replace McCausland with Vaclav Cerny at half-time, but he might have been left wondering if he should have made a change on the other wing when Jefte got his marching orders.
The decision from Italian referee Marco Guida appeared harsh on the 20-year-old, but the summer arrival from Fluminense’s participation was always on a knife edge after an early first yellow.
As the possession statistics tipped in favour of the visitors, Ukraine midfielder Karavayev dragged a shot wide on the break.
Rangers applied some intense pressure of their own despite being down to 10 men but were undone when midfielders Pikhalyonok and Voloshyn exploited the growing spaces left by the hosts.
Rangers started their temporary stint at Hampden with a 2-1 Premiership victory against Motherwell on Saturday and will have been disappointed with the number of empty seats for their first home European tie at the national stadium.
There were some disgruntled noises among the home support when it was announced McCausland would start instead of Cerny, who scored his first Rangers goal at the weekend.
Clement revealed that medical staff ruled the recent signing was not yet ready to start two games in a week, but with Jefte replacing Scott Wright, the new men on the wing proved to be Rangers’ two most dangerous players in the first half.
McCausland can count himself unfortunate to be hauled off at the break, but Cerny showed his class and the Czech Republic international’s introduction could have swung the game had Rangers not lost a body on the opposite wing.
To make matters worse for the hosts, left-back Ridvan Yilmaz had to be taken off on a stretcher late on.
Captain Vitaly Buyalskyi had returned to the Kyiv midfield for Friday’s 2-1 win over Veres Rivne and was one of only four players to retain their places after Oleksandr Shovkovskyi took the chance to rest most of his first-leg starters for their domestic season opener.
Even with their talisman back, Kyiv did not look like a side capable of the impressive 9-2 aggregate victory over Partizan Belgrade in the previous round.
Kyiv’s head coach had also started Vladyslav Dubinchak ahead of Kostyantyn Vivcharenko and most of Rangers’ first-half threat came from the area patrolled by the new left-back.
That was probably high in Clement’s thinking as he introduced the more experienced Cerny at the break, but the red card was more decisive and Rangers will be left thinking they missed a golden opportunity against fairly ordinary visitors to go a step closer to the riches of the Champions League.
