The 30-year-old's first-half strike put Spurs on course for a 2-0 win in the Europa League in Russia, moving him within a goal of Martin Chivers' club record European haul of 22.
It was Defoe's seventh strike in four starts this season, although it has so far not been enough to persuade Villas-Boas to start him in the Premier League.
Villas-Boas has preferred big-money signing Roberto Soldado as a lone striker and he appears set to replace Defoe in the starting line-up against West Ham.
"We have to judge recovery and the fact that JD was involved today and Soldado wasn't," Villas-Boas said. "Everything will come into consideration.
"We have been extremely happy with the performances of both. It is a question of deciding what is best for the team.
"It was another great goal, a great finish. It's really good to see him out there again doing extremely well whenever he's given the opportunity.
"He is a great professional, has a great attitude and now he's only one off Martin Chivers so it's a real great achievement for him.
"I think he has the ambition this season to go even further up the ladder in this record tally behind Martin Chivers and as a all-time goalscorer so I think that plays highly in his motivation, definitely."
Defoe put the north Londoners ahead after 34 minutes, with Nacer Chadli sweeping home five minutes later to wrap up a 2-0 win.
Anzhi returned revitalised after the break but Spurs held strong, as their run without conceding in this year's competition stretched to a fourth match.
The only negative on the night was a knock sustained by Younes Kaboul, forcing him off 20 minutes from time at the Saturn Stadium.
The Frenchman has been plagued with injuries for the best part of 18 months and suffered another setback in Russia.
"It's a bit of a problem because of his injury in the knee it has taken him time for his body to adapt to new positions on his run," Villas-Boas said.
"Because of that he's putting extra strain on his muscles and keeps getting small contractions that limit him finishing the games.
"At the moment it doesn't look very serious but it will force him to stop for a week or so.
"When we get him back we will give him a one-week or two-week preparation to be physically better."