The visitors defeated Dinamo Tbilisi 3-2 on aggregate to reach this stage, and they will be hopeful of returning from Stadion Maksimir with a positive first leg result.
Match preview
Dinamo Zagreb have become seasoned veterans through the qualifying rounds of Europe's elite competition, having navigated their way through to the group stage of the Champions League in six of the last 12 seasons.
However, they have gone on to finish bottom of their group on all six of those occasions, including last season when only managing to collect four points alongside Chelsea, AC Milan and Red Bull Salzburg.
Despite replacing former Croatia boss Ante Cacic with former Liverpool midfielder Igor Biscan - who won this competition with the Reds in 2005 - in April earlier this year, Croatia's most successful club managed to extend their record number of Prva HNL titles to 24 by winning their sixth consecutive domestic championship.
However, they suffered a disappointing opening day defeat at home to their closest rivals from last season in the form of Hadjuk Split on Friday, with Marko Livaja levelling his compatriot Bruno Petkovic's opener, before Rokas Pukstas snatched all three points for his side in injury-time.
As such, Biscan will be determined to bounce back with a victory on Tuesday, as he will not want to see his side make the long journey to Kazakhstan requiring a victory to progress.
Astana, on the other hand, have only made it through to the Champions League group stage on one occasion, which was when finishing bottom of their group in the 2015/16 season.
They dominated the Kazakhstan Premier League between 2014 and 2019, winning six consecutive titles like their forthcoming opponents in their country, before missing out with third and second-placed finishes in 2020 and 2021 respectively.
However, they reclaimed their crown last time out, ultimately edging out Aktobe by a solitary point, but they missed an excellent opportunity to leapfrog Ordabasy at the summit by drawing 0-0 at home against Atyrau on Saturday.
Now managed by former CSKA Moscow assistant coach Grigori Babayan, the 43-year-old would have been delighted by his side's spirit to come from behind and knock out Dinamo Tbilisi in Georgia last week, providing confidence that they can produce a similar result in Croatia on Tuesday.
Dinamo Zagreb Champions League form:
Dinamo Zagreb form (all competitions):
L
L
D
L
L
L
Astana Champions League form:
D
W
Astana form (all competitions):
L
L
D
W
Team News
Dinamo Zagreb will remain without Gabrijel Rukavina due to an ongoing ankle issue, but otherwise Biscan appears to have a clean bill of health to select from.
After seeing his side throw away a one-goal lead to lose in their opening game of the season on Friday, the 45-year-old may turn to natural centre-back Dino Peric in order to shore up his side's defensive unit.
Astana, meanwhile, will have their club captain Abzal Beysebekov available again after the right-back missed his side's league game against Atyrau at the weekend due to suspension.
The 30-year-old scored a crucial equaliser against Dinamo Tbilisi in the first round of qualifying last week, before Dembo Darboe bagged what proved to be the winner only one minute later. It would be a surprise to see Babayan deter from naming the same starting XI.
Dinamo Zagreb possible starting lineup:
Livakovic; Moharrami, Peric, Sutalo, Ljubicic; Bulat, Misic; Spikic, Baturina, Ivanusec; Petkovic
Astana possible starting lineup:
Condric; Marochkin, Tomasevic, Amanovic; Beisebekov, Jovancic, Ebong, Vorogovskiy; Tomasov, Ourega; Darboe
We say: Dinamo Zagreb 3-1 Astana
Dinamo Zagreb will be aiming to provide themselves with some breathing space ahead of making the lengthy journey to Kazakhstan for the second leg of this tie next week.
There is little doubt that the Croatians have much more individual quality than Astana, and we can envisage them winning by a couple of goals to increase their chances of making it through to the third round of qualifying.