Qarabag ended a run of four consecutive home defeats in the Champions League
Qarabag became the first Azerbaijani side to record back-to-back Champions League wins as they beat Copenhagen.
Captain Abdellah Zoubir was in the right place to slot home the opener after Pedro Bicalho's shot struck the woodwork in the 28th minute.
Former Southampton forward Mohamed Elyounoussi almost equalised immediately as the Danish visitors surged forward on the counter, but he sent his shot wide.
However, the hosts settled the outcome in the 83rd minute when substitute Emmanuel Addai fired into the bottom corner from the edge of the box.
Former Hibs loanee Zoubir could have opened the scoring earlier when his shot brushed against the side-netting after Copenhagen full-back Rodrigo Huescas was caught on the ball.
Visiting goalkeeper Dominik Kotarski also produced two brilliant saves in quick succession, pushing Oleksii Kashchuk's curling strike wide and then flying high to send Zoubir's header over when it looked destined for the top corner.
Leandro Andrade's fierce strike towards goal was then well blocked by Marcos Lopez as Qarabag continued to dominate the first half.
Copenhagen grew into the game after the break with Jordan Larsson having a header saved, and then a Gabriel Pereira header crashing off the crossbar moments before Addai made it 2-0.
With Qarabag having beaten Benfica in their first tie, Azerbaijan are the 24th nation to have a team win successive Champions League games - and first new one since Moldova in 2021, when Sheriff Tiraspol did so.
Qurban Qurbanov's side travel to Athletic Club for their third Champions League fixture on October 22 (17:45 BST), while Copenhagen host Borussia Dortmund the day before (20:00 BST).
Watch highlights of every Champions League game from 22:00 on Wednesday on BBC iPlayer and the BBC Sport website and app.
There will also be a Champions League Match of the Day on BBC One on Wednesday, from 22:40 to 00:00.
