Oleksandr Pikhalyonok and Nazar Voloshyn s late goals secured Dynamo Kyiv a 2-0 second-leg win over 10-man Rangers, sending them into the Champions League play-offs 3-1 on aggregate.
Jefte was sent off for the hosts early in the second half, and they will have to settle for Europa League football after conceding twice in the last 10 minutes.
There was little to separate the teams in the first half, though Ross McCausland wasted his chance to break the deadlock, failing to catch his shot properly.
The turning points came either side of half-time – Jefte caught Andriy Yarmolenko late to receive his first booking and was harshly given his marching orders five minutes into the second half after an aerial challenge with Oleksandr Karavaev.
Vaclav Cerny tried to provide a spark for the Gers, but the hosts failed to take any chances before Pikhalyonok cut inside from the right to fizz a low shot into the bottom-right corner to put Dynamo in front.
Just two minutes later, Rangers were upfield and Voloshyn did brilliantly to keep the ball in play before finishing off a one-two with Mykola Shaparenko by firing a first-time shot past Jack Butland.
«Динамо» перемагає «Рейнджерс» і виходить у раунд плей-оф кваліфікації Ліги чемпіонів
Наш наступний суперник – австрійський «Зальцбург»
Рейнджерс : Динамо
— FC Dynamo Kyiv (@DynamoKyiv)
Data Debrief: Shovkovskyi s impact subs
Rangers played 40 minutes with 10 men but did not really come under any pressure from Dynamo until much later in the game.
Just one week ago, it was Cyriel Dessers scoring a 94th-minute equaliser to keep Rangers hopes alive, but this time, it was the hosts who fell victim to a late lapse in concentration.
