The Senegal striker scored with the last touch of the game to give Newcastle a 1-0 win on aggregate and on the night at St James' Park.
The Magpies had been playing against 10 men since early in the second half when Mehdi Carcela-Gonzalez was sent off but the winner looked as though it wasn't going to come.
The Russian side had been the better team in the first half and had the first chance when Samuel Eto'o dragged a low shot wide of the far post.
Alan Pardew's men were sloppy at times, with Cheick Tiote and Mapou Yanga-Mbiwa both giving the ball away on the edge of their own area to allow Guus Hiddink's side further chances before the break.
But the home side came out with more purpose after the interval as Moussa Sissoko missed two headed opportunities within minutes.
And the game really swung in their favour when Carcela-Gonzalez received two yellow cards in quick succession, the second for a needless foul on Massadio Haidara.
Newcastle, who lost Yohan Cabaye to injury early on, dominated possession from that point but their attempts to break down a resilient Anzhi side looked clumsy at times and the visitors retained their threat on the counter-attack.
Mbark Boussoufa even went close to scoring the away goal that would have ended Newcastle's hopes with just minutes left when his free-kick hit the underside of the bar with Rob Elliot beaten.
But just when the game looked to be heading for extra time after three goalless hours of football over both legs, Sylvain Marveaux crossed from the right for Cisse to send St James' Park wild.
|Newcastle United||Team Statistics||Anzhi Makhachkala|
|0||1st Half Goals||0|
|3||Shots on Target||1|
|7||Shots off Target||7|
|57.9||1st Half Poss.||42.1|
|67.7||2nd Half Poss.||32.3|