After beating FK Qarabag 1-0 in Glasgow last week, they held on to their aggregate lead on a sweltering night at the Tofiq Bahramov Stadium.
Celtic now go into Friday’s draw for the final preliminary stage and will be seeded as they seek a return to the group phase after missing out last season.
Celtic will face one of five opponents in the play-offs; Astana from Kazakhstan, Israeli side Maccabi Tel Aviv and Swedish club Malmo could meet Ronny Deila’s side. Serbian champions Partizan Belgrade and Skenderbeu – who are from Albania – are the other possible foes.
Although their ball retention was poor against the Azerbaijani title holders, the Parkhead side were rarely troubled.
Having conceded 24 goals in 14 European games last season, they kept a third clean sheet in four so far this term to secure progression.
Deila said: ”I’m very, very happy. It was an exciting game, right to the end there was so much nerves. I am proud of the team spirit that we had tonight.
“The midfield won balls all over the pitch and the defence was tight behind them. Defensively we were very, very good.
“Offensively we should have punished them more when we won the ball in so many good situations.
“But it was hot out there and the players got tired against a good team when they kept the ball. I’m just very happy and proud of the boys.
“Last season we talked about losing too many goals. In the league we were very good in defence and now we have also done it in Europe and that is a very good improvement.”
The dates for play-off first leg are 18/19 August with the second legs taking place on 25/26 August. The winning teams progress to the group stage, the losing sides enter the group stage of the Europa League.