Meeting at Tofiq Bahramov Stadium, before next week's return in Switzerland, both teams will seek to take a significant step towards the third round; the tie's losers being consigned to the Europa League.
Match preview
Trailing by a goal going into the second leg of their opening round clash with Lech Poznan earlier this month, Qarabag made full use of home advantage to eliminate the Polish champions. Indeed, they overturned their deficit by half time; going on to triumph 5-1 by the final whistle.
Gurban Gurbanov's side therefore stormed through to the next stage of the process, with Brazilian forward Kady - who netted five goals in last season's Europa Conference League campaign - scoring twice in their remarkable success.
As a result, the Baku-based outfit's latest attempt to reach the Champions League proper for just a second time remains alive: Qarabag were the first Azeri club to advance to the group phase of Europe's top tournament, back in 2017.
Long-serving coach Gurbanov, who led his side to the knockout stage of last season's inaugural Conference League, returned his side to top spot in the Azerbaijan Premier League last term, having previously failed to claim the title for the first time in eight years.
Also completing a double by winning the cup in May, the Horsemen are undoubtedly top dogs in domestic competition, but now seek more success amid Europe's elite.
FC Zurich, meanwhile, have also made the Champions League group stage just once before - back in 2009, when they finished fourth behind Real Madrid, Milan and Marseille.
The Swiss Super League champions, whose defence of their domestic crown began with a crushing defeat on Saturday, were also twice European Cup semi-finalists in the earlier decades of continental competition.
Eliminated by Liverpool and Madrid on those occasions, Franco Foda's current side would love to rub shoulders with such European heavyweights this term, after an absence of four years from any UEFA competition.
However, they must bounce back quickly from the disappointment of losing 4-0 on Saturday to Young Boys, who they finally usurped as Swiss champions last season.
That represented a second setback in succession, with Zurich being beaten 3-2 by Stuttgart in their final pre-season friendly, which had followed four consecutive warm-up wins.
Qarabag FK Champions League form:
Qarabag FK form (all competitions):
FC Zurich form (all competitions):
Team News
Given their spectacular success last week, Qarabag are set to name a similar starting XI for the visit of Zurich.
That would see Marko Jankovic continue in central midfield, after making his first competitive start since joining from Hapoel Tel Aviv earlier this summer - Richard Almeida and Qara Qarayev will battle it out to partner the Montenegro international in the hosts' engine room.
Brazilian winger Kady - the club's most expensive signing - provides their chief threat, in a three-man support cast for Ibrahima Wadji up front.
Meanwhile, Zurich could again be without centre-back Becir Omeragic due to injury, after the highly-rated defender missed the visitors' opening league game at the weekend.
Like Italy forward Wilfried Gnonto, Omeragic has been heavily linked with a move away from the club during the current transfer window, but the former should still start in attack, alongside Benin international Tosin Aiyegun.
Qarabag FK possible starting lineup:
Magomedaliyev; Vesovic, Medina, Medvedev, Bayramov; Almeida, Jankovic; Kady, Ozobic, Zoubir; Wadji
FC Zurich possible starting lineup:
Brecher; Kamberi, Kryeziu, Hornschuh; Conde; Boranijasevic, Krasniqi, Guerrero; Marchesano; Aiyegun, Gnonto
We say: Qarabag FK 1-1 FC Zurich
Both sides carry a goal threat and are used to taking the initiative in domestic competition, so there could be several opportunities at either end in this first leg.
Qarabag have proven themselves dangerous opponents in Baku, so they should at least travel to Switzerland next week on level terms.