The Frenchman, making his first appearance since tearing a hamstring at Fulham on December 10, was played in on goal by compatriot Yohan Cabaye with 64 minutes gone, but could not beat goalkeeper Vladimir Gabulov with an ambitious chipped effort.
An away goal would have seen the Magpies take a significant step towards the quarter-finals, although had keeper Rob Elliot, once again deputising for the injured Tim Krul, not made two excellent saves from Samuel Eto'o either side of half-time, Anzhi Makhachkala could have been heading for St James' Park next week with a lead to defend.
In the event, Alan Pardew would have been the happier of the two managers after seeing his much-changed side cope with the artificial pitch and plummeting temperatures at the Luzhniki Stadium to deny the hosts a home victory in Europe for the first time in eight attempts this season, and give themselves every chance of progressing.
However, he will need no reminding that Metalist Kharkiv left Tyneside last month with a 0-0 first leg draw, but did not make it through to the last 16.
Anzhi ran out having not lost a European game on Russian soil - their only defeat came against Rangers in the 2001-02 season in a game played on neutral territory in Warsaw - and having only conceded their first home goal against Hannover in the previous round.
That record, combined with the pitch and the weather - it was -5 in Moscow at kick-off time - suggested the Magpies would have their work cut out.
Pardew was without six members of his strongest side with Krul, Fabricio Coloccini, Mathieu Debuchy, Jonas Gutierrez, Yoan Gouffran and Papiss Cisse left behind for a variety of reasons, and he chose to leave Steven Taylor, Davide Santon and Cheick Tiote sitting on the bench.
That meant fielding a starting XI without a single recognised striker as Ben Arfa was asked to lead the line.
In the circumstances, it was perhaps not surprising that the visitors failed to muster a single effort on target during the opening 45 minutes.
But to Pardew's delight, Anzhi were little more threatening in a half which did little to excite a sparsely-populated stadium.
Newcastle's cause was helped in no small part by £30million Brazilian Willian's premature departure through injury.
In the 23 minutes he was on the pitch, he looked the man most likely to cause the Magpies problems, feeding a telling 14th-minute pass into the path of Oleg Shatov to prompt a timely intervention by Mapou Yanga-Mbiwa, and then drilling and shooting from a tight angle well wide seconds later.
Eto'o was left appealing in vain for handball against Massadio Haidara after breaking from his own half with 29 minutes gone with Hungarian referee Istvan Vad unmoved.
Newcastle featured as an attacking threat only fleetingly with Gabriel Obertan keeping full-back Andrei Eschenko occupied at times, but without looking like opening the home side up.
In the event, it was Elliot who made the game's first save five minutes before the break, tipping Eto'o's dipping drive from distance over the bar.
Anzhi resumed in determined fashion and it took a brave block by central defender James Perch to prevent substitute Lacina Traore's shot from troubling Elliot.
Newcastle responded by mounting a rare cohesive attack as Moussa Sissoko found Ben Arfa and then set off in anticipation of a return pass, but central defender Ewerton stepped in.
Elliot turned Eto'o's skidding 61st-minute drive around the post, and Shatov acrobatically fired wide from the resulting corner.
But Ben Arfa was handed a glorious opportunity to give the visitors the lead three minutes later when he was played in by Cabaye, but saw his chipped effort easily blocked by Gabulov.
It proved to be the France international's final act of the night as he was replaced by European specialist Shola Ameobi.
Eto'o blazed a long-range free-kick high and wide as his frustration started to show, but it took a good block by Eschenko to keep stop Sylvain Marveaux's long-range effort.
Elliot had to field a scuffed effort from Eto'o as time ran down - and the visitors held on.