The Eredivisie side hold a 1-0 lead going into the second leg of their last 16 clash and are looking to extend their unbeaten run in the competition to 10 games.
Dick Advocaat's men topped Group L as they came through the first stage courtesy of wins against Shakhter Karagandy and Maccabi Haifa, as well as two draws against PAOK.
Having beaten Slovan Liberec over two legs in the last round, they now stand on the brink of a place in the last eight of the competition again after their run in 2011-12, although Advocaat will have to watch from the stands as he serves a one-game ban.
The 66-year-old was ordered from the dugout during the first leg after leaving his technical area to argue with Italian referee Daniele Orsato.
American forward Aron Johannsson struck the only goal of that game from the penalty spot, and AZ will be confident of progression despite Anzhi's recent revival at home.
Since their return from the mid-season break, Anzhi have not lost at the Stadion Saturn - although they will need to extend that with a first home win in Europe since October if they are to continue their run in the competition.
The Russian Premier League outfit are a different proposition to the side that once included Samuel Eto'o and Roberto Carlos - prior to their financial cut-backs that saw a mass exodus - and they only collected their first win of the league season earlier this month.
With owner Suleyman Kerimov having massively reduced the funds on offer to the club, they failed to win any of their first 19 league games, but the Europa League has been a welcome distraction.
They only lost twice in the group stages, both times to Tottenham, but qualified as runners-up and came through the last round against Genk with a 2-0 aggregate win.
