The Group A campaign, which starts Sep 20, will be the first serious test for Guus Hiddink’s side of their ability to deliver.
But Anzhi will not be overawed after charging through three qualification rounds scoring 15 goals and conceding none.
A 5-0 thumping of AZ Alkmaar in the second away leg of their playoff tie Thursday showed confidence was high.
Liverpool limped through their playoff relying on an 88th minute strike by Luis Suarez to beat Hearts 2-1 on aggregate.
Udinese dropped into the Europa League after Champions League elimination at the hands of Portuguese side Braga.
Rubin Kazan have been drawn with Inter Milan.
Partizan Belgrade and Neftci Baku, Azerbaijan’s first group stage representative, make up Group H.