The hosts need to match Sporting Lisbon's result this week before facing them on matchday six, while Rakow are already out, but can still keep hopes of a Europa Conference League spot alive if they win here.
Match preview
Dropping into the Europa Conference League always appeared the most likely outcome for both of these sides, but Sturm's fate is still in their own hands with two games remaining.
Should Sturm match Sporting's result here, they will need to win in Lisbon by a scoreline better than 2-1 - by a bigger margin or with more away goals scored - and they will leapfrog the Portuguese side in second.
Getting the job done here first is the most important thing though, and Christian Ilzer should feel confident his side can do so, considering their only win in the section so far came in Poland on matchday two.
Morale may have been lifted by a return to form domestically too, as back-to-back wins mean Sturm are currently level with Red Bull Salzburg at the top of the Austrian Bundesliga.
A win over Austria Lustenau on Saturday has kept them joint-top, and it was important to pick up where they left off before the international break, following a recent five-game run where their only win came against second-tier Grazer AK.
Rakow's task is much simpler - anything but a win here and they will be eliminated from Europe altogether this season.
The surprise Polish champions have struggled on their group stage debut, as their only point so far came against a Sporting side who played with 10 men for 85 minutes.
Despite a valiant effort in Lisbon on matchday four, an early red card of their own made the task insurmountable, as a 2-1 defeat ended any slim hopes they had of finishing in the top two.
Dawid Szwarga's side are slightly off the pace domestically too, and come into this one on the back of two straight 1-1 draws versus Pogon Szczecin and Cracovia.
With their next two league games both away trips to the top two - Slask Wroclaw and Jagiellonia Bialystok - their focus may be on those two matches.
Sturm Graz Europa League form:
L
W
D
L
Sturm Graz form (all competitions):
D
L
L
L
W
W
Rakow Czestochowa Europa League form:
L
L
D
L
Rakow Czestochowa form (all competitions):
D
D
W
L
D
D
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Team News
Luka Maric was given a first professional start at the weekend as Brighton & Hove Albion loanee Kjell Scherpen was missing in goal due to illness.
Central defender Gregory Wuthrich is also a doubt after missing the win against Lustenau, so Dimitri Lavalee may slot in at the back once more.
Elsewhere on the injury front, Otar Kiteishvili (Achilles) and Seedy Jatta (hip) will also miss out.
Bogdan Racovitan's red card in Rakow's defeat to Sporting on matchday four means the Romanian will be suspended for this clash.
Gustav Berggren missed the weekend draw with Cracovia and is a doubt for this one, so Ben Lederman may keep his place in midfield.
John Yeboah started in Lisbon, but is now recovering from a calf issue, so Szwarga will hope Bartosz Nowak is ready to start after three straight appearances from the bench.
Ivi, Kamil Pestka, Luka Zwolinski and Adrian Gryszkiewicz are all closing in on returns to the side, but Greek midfielder Giannis Papanikolaou is out until the new year with a shoulder injury.
Sturm Graz possible starting lineup:
Maric; Gazibegovic, Affengruber, Lavalee, Schnegg; Gorenc-Stankovic, Prass, Boving, Horvat; Sarkaria, Wlodarczyk
Rakow Czestochowa possible starting lineup:
V Kovacevic; Tudor, A Kovacevic, Rundic; Silva, Lederman, Kochergin, Plavsic; Nowak, Kittel, Cebula
We say: Sturm Graz 2-0 Rakow Czestochowa
After a win in Poland on matchday two, Sturm will be big favourites to win here to keep their hopes alive heading into matchday six.