Both goals were scored in the first half as the North Londoners built on their 3-0 win over Tromso at White Hart Lane with an assured performance away to Gadzhi Gadzhiyev's men.
Jermain Defoe opened the scoring, blasting the ball into the roof of the net in the 34th minute to move to within one goal of Martin Chiver's European record for Spurs, before Nacer Chadli doubled the advantage six minutes later.
Despite facing more pressure in the second half than it had in the first, Tottenham's defense was rarely troubled, meaning the North London outfit is still yet to concede in its continental campaign and retains its perfect record through two matches.
Villas-Boas continued with his policy of playing Defoe in the competition after he scored twice against Tromso last time out, while Zeki Fryers and Vlad Chiriches made their first European starts for the club.
Anzhi had gone three games without scoring a European goal prior to the clash and named forwards Pavel Solomatin and Serder Serderov alongside Islamnur Abdulavov up front, with Lacina Traore dropping to the bench.
After what was a subdued opening 10 minutes, Defoe had the first half-chance, firing just wide of Evgeni Pomazan's right-hand post. Despite continuing to enjoy plenty of possession, Spurs struggled to break down a resolute Anzhi defense, with their next sight at goal coming courtesy of Lewis Holtby just after the half-hour mark.
However, the visitors' patience was rewarded when Defoe hammered home after 34 minutes; Holtby slid the England international in with a neat pass and he made no mistake, putting Tottenham ahead with his fifth goal in this season’s competition.
Summer recruit Chadli then extended the lead five minutes before the break with his second goal in a Tottenham shirt. The midfielder coolly slotted past Pomazan after good work from Kyle Walker to put Villas-Boas’ men firmly in charge.
The Belgium international curled narrowly wide from outside the area shortly after the restart as he went in search of a second goal, before Andrei Eschenko forced Hugo Lloris into a save with his cross-shot from the left-hand side.
The French goalkeeper was called into action twice more in quick succession, as he first parried away a Solomatin shot before punching away the resulting corner as the hosts showed their attacking capabilities for the first time in the match.
Solomatin again threatened late on, this time with a dipping drive, but Tottenham saw the game out with relative ease to record back-to-back victories in Group K.