Two weeks ago the reverse fixture took place at Anfield, with the Reds triumphing 1-0 thanks to a Stewart Downing goal.
That win put Liverpool top of the group, but it might be something of a different team that the Reds put out for this game with Chelsea awaiting in the Premier League on Sunday.
Though Anzhi are based in Dagestan, the match will take place in Moscow. Liverpool will nonetheless have a big challenge ahead of them to come out of the match with anything at all—though they know even a point would put them a big step closer to qualification for the knockout rounds.
Here are the five key battles of the match.
Anzhi captain Samuel Eto'o will be expected to lead the attack for his team and deliver the goals that were lacking at Anfield.
He could try to latch himself onto the less-mobile Jamie Carragher; it will be up to Liverpool to adequately ensure that Seb Coates is able to do the job, either in the first instance or if not then covering behind Carragher when Eto'o is able to outpace the defender.
Coates is a good reader of the game, unafraid of making a tackle, is strong in the air and generally composed enough to show himself as a top defender.
He arguably deserves more chances to show his abilities in league play.
Lacina Traore was only on the bench in the Anfield match but should be restored to the starting lineup in Russia.
Traore is a tall, powerful and awkward-looking striker but he certainly has goals in him—eight so far in the Russian Premier League, though he has yet to net in Europe.
Jamie Carragher will have to use all his experience to keep the Ivory Coast forward at bay, but is still capable of doing the job despite being used less and less with every passing month.
The Reds will probably play a deeper defensive line than usual for spells of this game; it will suit Carragher, but will probably suit Traore as well from an attacking perspective.
Chris Samba is a powerful defender, good at organising and superb in the air.
Liverpool don't have a recognised senior striker to send to Russia with Luis Suarez left at home and Fabio Borini injured.
The Reds may give another start to young German striker Samed Yesil, Spanish under-21 forward Dani Pacheco or indeed try another player in the central role. Given the relative lack of pace at the back for Anzhi, perhaps they would let Oussama Assaidi loose in a free role that would be ideal for playing on the counter?
Whoever is given the nod, Liverpool need that player to put in a good performance. With a number of first-team regulars missing, the away team are likely to come under sustained pressure during spells of the match and will have to be both creative and clinical when they have the opportunity to trouble the home side.
A first Liverpool goal for any of the three mentioned here might go some way to securing qualification—or perhaps Joe Cole might fancy one last stab at redemption?
The midfield battle will be an intriguing one to watch as both teams try to control the match—Anzhi because they realistically need a win and will be expected to triumph at home, and Liverpool because they will want to keep themselves in possession and building their preferred route to goal through a patient approach.
Jordan Henderson has been shifted around the Liverpool team a lot this season, playing both right and left side as well as, most recently, at right-back and right wing-back.
Against Anzhi he should finally get a chance to move back into his natural position, the centre of midfield.
For his own first-team prospects as well as the needs of the club, he'll be required to have an excellent match.
It will undoubtedly be a relatively tight match, which if neither side plays at their best could give rise to few opportunities on goal.
Later in the game, both managers will likely turn to their substitutes bench for inspiration to win the match—but who will be on it for Liverpool?
Anzhi may have the likes of Jucilei or Georgiy Gabulov waiting to enter; Liverpool are more likely to send the likes of Joe Cole and perhaps a few untried youngsters, such as Michael Ngoo or Jordan Ibe.
Which boss makes the right decision, at the right time, could be the difference between defeat and a draw—or even a win.