Group K always looked like it would be a cakewalk for Spurs, who came through their toughest test 2-0 victors thanks to Defoe and Nacer Chadli strikes in the first half on the outskirts of Moscow.
It was an impressively comfortable performance from Andre Villas-Boas' heavily-rotated side, which was still awash with star quality unlike the hosts.
Anzhi's big-spending was brought to an abrupt halt in the summer, leading to a dramatic firesale that meant there were only three survivors from the side that started March's last-16 clash at Newcastle in tonight's line-up.
Such changes have seen the Russian side fail to collect a single win this season - a run that looked certain to continue when Defoe clinically fired Spurs ahead after 34 minutes.
The hardy 150 travelling fans were celebrating once again five minutes later, with Kyle Walker collecting a Lewis Holtby pass and squaring for Nacer Chadli to sweep home.
Anzhi returned for the second-half rejuvenated but Spurs held firm, as their run without conceding in this year's competition stretched to a fourth match.
The result was not surprise given the way 'The Anzhi Project' has spectacularly unravelled in recent months.
Billionaire owner Suleyman Kerimov significantly withdrew his backing in August, leading the likes of Samuel Eto'o, Willian and Lassana Diarra to head for pastures new.
If that was not bad enough, Anzhi have been forced to play European matches away from Makhachkala due to the current conflict in Dagestan.
It meant the Group K clash was held 1,100 miles away at the Saturn Stadium in Ramenskoye on the outskirts of Moscow.
A fair number of Anzhi fans 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 mintues, 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.
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.
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 pullback.
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 was guilty of a dive 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.
Lloris parried away a Solomatin effort as Anzhi searched for a late consolation goal, which never came as Spurs held out for a decent win in tough conditions.