Last week's 0-0 draw in Moscow preceded another fairly dour struggle in Northeast England which saw a dramatic second half with Anzhi losing a man and also hitting the crossbar from a free-kick.
Papiss Cisse was again the hero for the Toon, netting a 94th minute winner to send Alan Pardew's men through to the quarter-finals where they will be drawn against either Chelsea, Tottenham, Benfica, Rubin Kazan, Lazio, Basel and Fenerbahce.
Guus Hiddink's Anzhi were reduced to ten men when Mehdi Carcela-Gonzalez was sent off for a second yellow card for a foul on Massadio Haidara but Newcastle were unable to capitalise until the final kick of the game.
That could have almost been a different story when Mbark Boussoufa struck the woodwork with his 22-yard free-kick before Cisse saved the day for the Magpies by firing home Sylvain Marveaux's tempting cross to add to his injury-time winner against Stoke City on the weekend.
The draw for the Europa League quarter-finals will take place in Nyon, Switzerland tomorrow with the first legs to be played on April 4 and second legs taking place on April 11.
2012/13 UEFA Europa League - Round of 16 second leg
St James' Park, Newcastle-upon-Tyne - 45,487
Red card:ANZ - Mehdi Carcela-Gonzalez 55'