Jermain Defoe opened the scoring with a clinical finish in the 34th minute and Nacer Chadli turned in a Kyle Walker cross five minutes later to double Spurs’ advantage.
Anzhi battled hard after the interval in an effort to get back into the game but Tottenham never looked like relinquishing their lead and held firm to maintain their strong start to the season.
Anzhi’s big-spending was brought to an abrupt halt in the summer, leading to a dramatic fire sale that meant there were only three survivors from the side that started March’s last-16 clash at Newcastle in the line-up, while Andre Villas-Boas rung the changes for Tottenham.
There was a subdued atmosphere at the Saturn Stadium in Ramenskoye on the outskirts of Moscow, 1,100 miles away from Anzhi’s home after they were forced to play European matches elsewhere due to the current conflict in Dagestan.
A fair number of Anzhi fans had made the long trip north and looked set to be rewarded by an early goal, only for Pavel Solomatin to be adjudged – perhaps harshly – offside before he could round Hugo Lloris.
Spurs were soon on top, though, with Walker getting a lot of joy down the right flank as the hosts sat back.
Defoe hit the north Londoners’ first chance of the night wide after 11 minutes, with Sandro attempting a similar effort soon after.
Villas-Boas’ side were keeping possession with ease as the pitch began to cut up, with Anzhi resorting to hitting it long when they got the ball.
Lewis Holtby forced Evgeni Pomazan into action with a left-footed curling effort from 20 yards, before Tottenham finally found the opener in the 34th minute.
Holtby played a fine ball to Defoe in the box, allowing the striker to rifle home into the roof of the net and move one goal away from Martin Chivers’ club record European haul of 24.
Five minutes later and Spurs seemingly had three points wrapped up. Again Holtby was involved, playing the ball out to Walker, with the right-back slipping the ball across to Chadli to sweep home his second for the club.
There could have been another as half-time approached, only for Defoe to miskick after a Walker pull-back.
Anzhi brought on reported Liverpool target Lacina Traore at the break and it led to an improved second half for the hosts.
Lloris reacted well to clear a low cross-shot from substitute Andrei Eschenko and then palmed over a drive from Solomatin, who slipped under a challenge from Younes Kaboul.
The French defender looked in discomfort immediately after the incident and was replaced by Michael Dawson for the last 20 minutes.
Long-range Chadli and Holtby efforts were all Spurs had to show for their second-half display, before Defoe fired wildly over in the 83rd minute.