Leading 1-0 from the first leg last week in Glasgow, Ronny Deila’s side never looked like extending that margin as they often found themselves on the back foot.
But they delivered a professional performance and held firm to ensure they will be one of the five seeded teams in the ‘Champions’ section of Friday’s draw.
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.
Despite much pre-match focus on the poor state of the pitch at the Tofiq Bahramov Stadium, it caused no major problems as a tense 90 minutes was played out.
Celtic were made to work hard for the narrow advantage they took to Azerbaijan and it was no surprise they found themselves under siege from the start.
While the hosts had much of the ball, however, they struggled to carve out clear-cut chances against a disciplined visiting defence.
Virgil van Dijk cleared from Reynaldo when he tried his luck from long range then was in the right place to usher out for a goal kick when Ilgar Gurbanov tried to find Alharbi El Jadeyaoui.
The Dutchman was also well placed soon after as he got in Rydell Poepon’s way then even tried attacking himself but was foiled after a good run took him past four home players.
As time went on, Celtic began to settle and Stuart Armstrong found space but his inviting ball was cleared by Rashad Sadygov before anyone could connect.
Back came Qarabag, who almost had their fans in raptures when Craig Gordon didn’t come for a cross but Emilio Izaguirre bailed him out and it remained goalless.
The longer the Azerbaijani champions went without scoring, the more frustration set in and Gordon added to it as he pulled off an excellent save from Richard Almeida’s 20-yard shot.
Qarabag kept pushing forward and Celtic looked nervous as van Dijk had to step in yet again to put Dani’s shot behind for a corner but it was still 0-0 at the break.
The second half started slowly and that suited Deila’s men, who were still struggling to get forward and make openings.
They found it hard to get on the ball too and it was fortunate for them that Qarabag appeared to lack ideas when they got into the final third.
El Jadeyaoui was denied and Van Dijk did well to dispossess Reynaldo as the home team’s chances faded.
Celtic had a late chance to claim victory on the night too when Stefan Johansen shot just wide with their best chance but his miss didn’t matter and they progressed.