Jefte was harshly sent off for Rangers before two quick Dynamo Kyiv goals ended their Champions League hopes for another season.
Cyriel Desser’s last-gasp equaliser in the first leg had given Rangers hope and both he and Ross McCausland had chances to give them the lead early in the second leg of the third qualifying round tie at Hampden Park.
Already on a booking, Jefte was punished in the 50th minute with a yellow as he jumped to win a header and was shown a red card that made it a struggle for the hosts.
They held on for 30 minutes but Philippe Clement’s side eventually collapsed and substitutes Oleksandr Pikhalyonok and Nazar Voloshyn scored in quick succession to seal a 2-0 win on the night – 3-1 on aggregate – to send Dynamo through to the play-off to face RB Salzburg.
Heartbreak at Hampden
It was not a great night for Clement’s side who will see this as an opportunity lost as they drop into the less prestigious and certainly less lucrative Europa League group phase.
Rangers made a high-pressing start and the visitors initially looked uneasy in defence.
However, Oleksandr Shovkovskyi’s side worked their way into the game and in the ninth minute winger Vladyslav Kabaev sped past Rangers captain James Tavernier down the left but his inviting cross found no takers, to Rangers’ relief.
Rangers made little headway until the 20th minute when Jefte nodded a looping Tavernier cross past the far post, before thundering a snatched shot from 25 yards high over the bar minutes later.
A Dessers header from a Jefte cross was easily saved by Kyiv ‘keeper Georgiy Bushchan and then, as Rangers pressed, the ball fell to Tom Lawrence inside the box but he could not sort out his feet to get a shot away.
When they did attack, Kyiv looked pacey and purposeful which kept Rangers’ defence on a state of high alert.
In a Rangers counter just after the half-hour mark, Dessers played in McCausland but although his shot was parried by Bushchan, Clement’s side failed to take advantage of the loose ball.
Cerny replaced McCausland for the start of the second half which gave Rangers fans reason for optimism but that disappeared when Jefte, booked for a touchline foul on Andriy Yarmolenko after 30 minutes, was cautioned again and sent packing for an aerial challenge on Oleksandr Karavaiev.
When the dust had settled on what looked like a soft second yellow, and the Rangers fans cranked up the noise in defiance, Karavaiev raced clear of the defence but screwed his shot wide.
Kyiv took advantage of the extra player and moved with menace before Rangers rallied, and the game swung end to end.
In the 68th minute Dujon Sterling replaced tiring midfielder Mohamed Diomande and Ben Davies took over from Ridvan Yilmaz, who was taken from the field on a stretcher after picking up an injury after taking a shot minutes beforehand.
It was another blow for the Light Blues and Dessers seemed to take umbrage with the fans after hearing groans and moans when he lost possession when he had no support.
Rangers ‘keeper Jack Butland was hardly under fire but he did save a long distance effort from Taras Mykhavko.
However, in the 82nd minute, he had little chance when Pikhalyonok fired in from distance under no pressure from the Rangers defence.
Voloshyn then converted a cut-back from Mykola Shaparenko to seal the tie, with Butland rescuing himself at the end when he saved a shot from Vladyslav Vanat, after his initial mistake.
What’s coming up for Rangers?