The 31-year-old's slightly deflected effort helped to secure a hard-fought 2-0 win at Sheriff Tiraspol, putting Spurs on the cusp of qualification to the Europa League knockout stages.
It was Defoe's sixth in the competition this season and saw the England international move level with Chivers in the club's record books.
Fans' favourite Chivers was part of Tottenham's UEFA Cup-winning side of 1972 and said in the build-up to Thursday's clash that Defoe deserves to break his record.
The former England international said Defoe had "earned everything he's done" and boss Villas-Boas was full of praise after his latest strike.
"It is some achievement," the Portuguese said. "If we continue like this, there is a big chance he will break the record.
"It will be another great achievement for him. I am sure he will achieve it.
"Let's not celebrate it before it happens, but it will be a great record for him and the club. It was another great performance by Jermain."
Defoe's strike came just at the right time for Spurs, as the hosts were seriously threatening to level the scores at Stadionul Sheriff.
Jan Vertonghen gave Spurs the lead after 12 minutes, but fellow defender Vlad Chiriches was forced to make a stunning block at full stretch to prevent Henrique moments later.
Cadu had a goal disallowed and both Ismail Isa and Richardinho came as Sheriff pushed for a leveller, only for Defoe to strike home shortly after Aaron Lennon had struck a post.
"They had some great opportunities on the counter-attack," Villas-Boas said. "I think in the counter-attack, you have to recognise that they were excellent.
"The game could have easily gone to 1-1 as after we scored they had so many chances to level the score.
"They looked good on the counter-attack, had some great moments and we have to recognise that.
"It is difficult to say, given the amount of chances.
"A draw would be a fair result, but the second goal is always important in games like so this, so both teams were creating.
"We were fortunate to get the second goal to kill the game, but it could have gone the other way."
The victory leaves Spurs top of Group K with maximum points and with five clean sheets from as many games in the Europa League this season.
They could have secured their place in the last 32 on Thursday night, but Anzhi's 1-0 defeat of Tromso means they will have to wait for Sheriff's trip to White Hart Lane on November 7.
"It was not easy," Villas-Boas added. "I think we deserved to take the lead but they counter-attacked extremely dangerously.
"We also had a lot of chances and could have gone 2-0 comfortably.
"In general, we did enough to win the game and get to nine points, which was the objective so we can achieve qualification at the next game."
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