The Senegal international, who fired the Magpies to a 2-1 Barclays Premier League win over Stoke on Sunday with a 92nd-minute strike, had to wait two minutes longer to power home Sylvain Marveaux's inviting cross with the final touch of an intriguing contest.
Anzhi, who had midfielder Mehdi Carcela-Gonzalez sent off in the second half, came close with two minutes of normal time remaining when Mbark Boussoufa's free-kick came back off Rob Elliot's crossbar. But on a night of high drama on Tyneside, Alan Pardew's men booked their place in Friday's draw for the last eight in Nyon in front of a crowd of 45,487.
The early momentum was largely with Anzhi and had it not been for Magpies defender Steven Taylor, they could have taken the lead on several occasions.
Taylor kept Lassana Diarra at bay three times inside two minutes with the midfielder being allowed to run deep into enemy territory unchecked - and he put his body on the line once again to prevent Silva Jucilei's firmly-struck drive reaching Elliot.
The Magpies' efforts to trouble opposite number Vladimir Gabulov were tepid with Yohan Cabaye having earlier prompted him into his only save of note, and even that did not trouble him to any great extent. The France international later limped off with a groin injury.
The situation might have worsened dramatically within seconds when Eto'o pounced on an error by Mapou Yanga-Mbiwa to feed Odil Ahmedov, whose shot rippled the side-netting.
Newcastle should have been ahead when Marveaux's free-kick came off Cisse and fell nicely for Taylor - but the defender could only stab the ball straight at Gabulov.
The momentum had shifted and it moved further in the Magpies' direction three minutes later when Carcela-Gonzalez, booked earlier for a foul on Cheick Tiote, caught Massadio Haidara and received a second yellow card.
The Magpies got lucky when Boussoufa rattled the crossbar with a free-kick from 22 yards with Elliot beaten, before they won the tie with the last touch of the game when Cisse powered Marveaux's cross past Gabulov.