The team now have maximum points in Group K of the competition - scoring 12 goals in four games (including the play-off) and yet to concede.
Jermain Defoe opened the scoring with a powerful trademark finish, with Nacer Chadli effectively putting a seal on events with a second before the break. Anji did rally in the second half but could not find a way past the excellent Hugo Lloris.
Both teams struggled to find a rhythm or pattern to their game in the opening ten minutes, although Anji were marginally the livelier and did threaten to get in behind our back line on a couple of occasions.
Defoe fired in our first effort on goal after 12 minutes, but dragged it slightly and it went wide of Evgeni Pomazan's right hand upright. Sandro then tried likewise from a little further out and did find the target, but Pomazan fielded with ease.
It was a cold evening in Ramenskoye - away from Anji's natural habitat - but not so cold that you expected blankets to be distributed around the media area. Perhaps it was a message on what to expect later in the second half.
Territory was being established and as 20 minutes approached it was firmly in the home half bar one half chance breakaway when Islamnur Abdulavov's sprint was quickly thwarted by Lloris.
Lewis Holtby then unleashed a curling effort that Pomazan did well to parry before the next wave of white came surging forward, with the centre under the control of messrs Sandro and Dembele.
It was just desserts when, on 34 minutes, Holtby picked out Defoe to the right of the area and the little hit man took aim and smashed past Pomazan high into the net to take him to 21 goals in European competition.
Four minutes later the advantage was doubled when Holtby picked out the run of Kyle Walker, who delivered a well placed low centre in the direction of the penalty spot. In position to capitalise was Chadli , who sidefooted past the despairing dive of Pomazan.
There was a big chance for a third after Walker again provided from the right, but both Erik Lamela and Defoe could not connect.
Benoit Angbwa shot wide in the opening exchanges of the second half before Chadli was also off target at the other end after good work from Lamela. Lloris then had to be his usual alert self to pounce on a low cross from Odil `Ahmedov. Lloris then brilliantly diverted a Andrei Eschchenko cross with his feet as Anji attempted to make a fight of it.
Pavel Solomatim then smashed goalwards and it took a superb tip over by Lloris to deny a halving of the deficit.
Younes Kaboul was struggling as the game neared the final 20 minutes, with Michael Dawson readied quickly to take over defensive duties. Gylfi Sigurdsson was also drafted in to replace Lamela.
The next change was the introduction of Christian Eriksen in place of the impressive Holtby on 78 minutes and the advantage remained in tact and thoughts turned to boarding a plane ready for the next challenge of West Ham at the Lane on Sunday.
Anji (4-2-3-1): Pomazan; Angbwa (Gadzhibekov, 78), Adeleye, Ewerton, Tagirbekov; Jucilei, Ahmedov; Solomatin, Razak, Serderov (Eschenko, 56); Adbulavov (Traore, 46). Subs not used: Kerzhakov, Grigalava, Gatagov, Demidov.
Spurs: Lloris; Walker, Chiriches, Kaboul (Dawson, 71), Fryers; Dembele, Sandro; Lamela (Sigurdsson, 71), Holtby (Eriksen, 78), Chadli; Defoe. Subs not used: Friedel, Naughton, Kane, Soldado.
Goals: Spurs - Defoe (34), Chadli (39).
Referee: Mr B Yildirim (Turkey).