It took a while for Spurs to take a stronghold in the match, but after a chance in the 13th minute, Defoe was eventually able to make it count around 10 minutes before half time by hammering the ball into the back of the net.
Chadli managed to make it two for the North London outfit just four minutes later by collecting a pass from Kyle Walker and beating the keeper in the penalty area.
After the break, Anzhi showed their intent by bringing on forward Lacina Traore, who was expected to miss the clash with a shoulder injury, but the attacker made a positive start to the second half.
The forward charged from his own half trying to find the breakthrough for the Russian outfit, gliding past Sandro and playing the ball wide to Andrey Yeshchenko, but Spurs goalkeeper Hugo Lloris managed to block the cross.
Minutes later, Lloris was called upon again to make a save when Pavel Solomatin fired the ball towards goal, forcing the Spurs keeper to push the ball out for a corner, which came to nothing.
Anzhi created a better start to the half, but Tottenham remained comfortable throughout and managed to survive a penalty shout when Solomatin fell to the ground in the box when Younes Kaboul placed his arm onto the Russian's shirt. The referee waved it away.
With 10 minutes left to play, Defoe was close to keeping up his record of two goals from every start this season, but his run was flagged offside when he retrieved the ball from a Gylfi Sigurdsson pass.
For Anzhi, they were unable to make an impact towards the closing stages of the game and went away empty handed.