The only goal of the game came in the final minute of added time in the second half, with Papiss Cisse heading home a brilliant Sylvain Marveaux cross to bring an exciting end to an otherwise gritty affair.
Newcastle boss Alan Pardew made three changes from the side who were held in Russia with Davide Santon, Steven Taylor and Cheikh Tiote all returning to the side, with Hatem Ben Arfa, Tim Krul and Fabricio Coloccini all missing out through injury.
The first chance of the night came when an adventurous run from right-back Andrey Yeschenko through the middle of midfield, ghosting past Vurnon Anita, saw him release Eto'o inside the box but the forward dragged his effort just wide.
A neat one-two down the right between Eto'o and Mehdi Carcela-Gonzalez carved open Newcastle's back four, with the former laying the ball across the box only to see Steven Taylor deny Lassana Diarra with a superb last-ditch tackle, the goal gaping after the ensuing scramble.
With the game opening up after the 15-minute mark, Mapou Yanga-Mbiwa lost out on the edge of his area to Diarra, who drove through in on goal only to see Taylor pull out yet another fantastic block to avert the danger with keeper Rob Elliot seemingly well beaten.
A suicidal quick free kick from Yanga-Mbiwa saw Odil Ahmedov intercept and play a quick one-two with Eto'o before driving his effort into the side netting, much to the relief of the French centre-back, with the scores remaining level at the break.
Newcastle raced out of the traps at the start of the second half, Moussa Sissoko nodding over at the near post. Moments later, Taylor missed a glorious chance after Cisse mistimed his volley in the box following a Marveaux free kick from out wide, the defender scuffing his effort straight at the goalkeeper.
The visitors were reduced to 10 men in the 55th minute when Carcela-Gonzalez went in late on Massadio Haidara to earn himself a second yellow but Anzhi still posed a threat on the counter, with Eto'o blazing a strike over the bar from outside the box almost immediately afterward.
A well-worked move by the hosts saw Tiote lash an effort over the bar from distance, while Mbark Boussoufa struck the bar with a free kick in the dying moments, but there was still time for one more twist in the tale.
Marveaux worked a yard of space down the right flank before sending in a magnificent cross into the box which Cisse nodded home just six yards out from goal. The Senegalese was rewarded with a rapturous reaction from the home crowd as Newcastle booked their place in the last eight of the competition with the final kick of the game.