The Premier League outfit seemed to settle quickly with fluid passing and composure on the ball but the longer it remained goalless, the more time Anzhi had to find their rhythm.
The first attack on goal came in the 15-minute mark when Oleg Shatov tried to cut the ball back from the left-hand side of the final third, but Mapou Yanga-Mbiwa was able to cover in time to clear it away.
The home side suffered a blow when Willian, who was looking a threat in the first 20 minutes, was forced off the field after crashing into advertising boards following a challenge from Massadio Haidara.
Lacina Traore, who scored against Liverpool during the group phase, was brought on to replace him, while the Magpies remained patient in the chilly conditions.
Haidara was made to work in the first half as he came up against Samuel Eto'o, who ran one-on-one with the defender, but Newcastle's January signing was able to close him down and clear the ball.
The home side were close to taking the lead in the final five minutes of the half when Eto'o struck the ball from 25 yards out straight into Newcastle keeper Rob Elliot, who was forced to tip the ball over the crossbar, allowing the visitors to breathe a sigh of relief.