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 tomorrow's draw for the last eight in Nyon in front of a crowd of 45,487.
Pardew was bullish as he approached the game, but was also swift to point out that while his side's 0-0 draw in Russia had been a good result, Anzhi still posed a major threat back on Tyneside.
He was to be proved correct as Guus Hiddink's men, despite the absence of injured Brazilian Willian, set about their task with some relish.
The visitors ran out at St James' Park knowing a score draw would send them through and from the off, they were positive as Mapou Yanga-Mbiwa struggled to get to grips with former Barcelona striker Samuel Eto'o.
The movement of Boussoufa, Odil Ahmedov and Jucilei behind Eto'o prove hugely problematic for the home side, who were hit on the break time and time again.
Eto'o might have fired the men from Dagestan ahead within three minutes after running on to full-back Andrei Eschenko's through-ball, but he dragged his effort across the face of goal.
Newcastle's response was swift and Marveaux, who started brightly, shot wide eight minutes later after cleverly avoiding challenges by Yuri Zhirkov and Jucilei wide on the right.
However, the 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 with 28 minutes gone to prevent 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.
But their hopes were dealt a significant blow eight minutes before the break when the France international limped off with a groin injury, the extent of which will be a major concern for Pardew.
The situation might have worsened dramatically within seconds when Eto'o pounced on an error by Yanga-Mbiwa to feed Ahmedov, whose shot rippled the side-netting.
Taylor headed a Marveaux free-kick high over at the end of the first half, but Newcastle headed for the dressing rooms knowing they had been comfortably second-best.
The home side returned in determined fashion and Moussa Sissoko headed Davide Santon's cross over within seconds of the restart. The former Toulouse midfielder should have done better four minutes later when he failed to connect with Marveaux's inviting cross in front of goal.
Newcastle should have been ahead with 52 minutes gone when Marveaux's free-kick came off Papiss 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.
Vurnon Anita was perhaps fortunate to escape with only a caution for his challenge on Yuri Zhirkov, but the visitors made light of their numerical disadvantage when Eto'o controlled a long ball and lifted a 59th-minute shot over Elliot's crossbar.
Tiote smashed a long-range effort just over 15 minutes from time with the home side dominating possession, but Eto'o forced a vital near-post save from Elliot seven minutes later.
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.