Liverpool, Sporting Lisbon, Qarabag, CSKA Moscow and APOEL Nicosia will advance to the Champions League group stage after the final qualifying round.
While five-time European kings Liverpool are returning to the continent's elite club competition after an absence of two years, Qarabag becomes the first team from Azerbaijan to reach the Champions League on Wednesday, reports Efe.
The Reds, 2-1 winners in last week's first leg away to Hoffenheim, scored three times in the space of 21 minutes in front of their supporters at Anfield to take the second leg 4-2 for a 6-3 aggregate victory.
Emre Can posted his first two-goal game as a professional while Liverpool newcomer Mohamed Salah and Roberto Firmino had one each.
Mark Uth and Sandro Wagner scored for Hoffenheim.
Sporting, who had to settle for 0-0 in the first leg in Lisbon, pounded Steaua Bucarest 5-1 in the Romanian capital, getting goals from Seydou Doumbia, Marcos Acuña, Gelson Martines, Bas Dost and Rodrigo Battaglia.
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Goals by Georgi Schennikov and Alan Dzagoev gave CSKA Moscow a 2-0 home win over Switzerland's Young Boys to bring the Russian's club advantage to 3-0 on aggregate.
Leading 2-0 after the first leg, APOEL Nicosia held Slavia Prague 0-0 on Wednesday to claim their spot in the 32-team Champions League group stage.
Qarabag, who won the first leg in Baku 1-0, lost 2-1 to Copenhagen in the second, but qualified for Champions play on the strength of their away goal, courtesy of Dino Ndlovu.
--IANS
sam/mr