Now in his second spell with the club, the 31-year-old struck home late in the 2-0 Europa League victory at Sheriff Tiraspol on Thursday evening.
It was Defoe's sixth European goal of the campaign and an effort that saw him draw level in the club's all-time scoring charts with Chivers.
Part of the UEFA Cup-winning side of 1972, the fans' favourite spoke fondly of Defoe ahead of the Group K clash with the Moldovan champions.
Chivers said "he's earned everything he's done" and would be a deserved record holder - comments that touched the England international.
"It is great to be top with Martin Chivers," Defoe told Press Association Sport.
"It is special because he is a legend at the club, someone I look up to and respect. To be up there is great.
"Someone told me about his comments - the fact he will be so happy for me if I get it.
"I bumped into him the other week after the West Ham game, had a little chat with him, a little bit of banter. He is a really nice guy. I have total respect for him.
"One more goal I will be on the top on my own, and to have someone around you like Martin Chivers is special."
Defoe's goal at Sheriff came at a good time for Spurs, who, despite taking an early lead through Jan Vertonghen, spent much of the match under pressure from the hosts.
"It was hard," Defoe said. "It was difficult because they were so organised and sat back.
"When you are a forward, you just want to get involved and get touches but it is a case of being patient.
"You have to stay calm, stay concentrated because you might get a chance in the first minute or the last.
"I got my chance towards the end and it was good to see it go in.
"I relish every game I play. It is not a case of worrying about what competition it is.
"Every game you play you've got to enjoy it, try to get the goals and most importantly win."
Defoe's slightly deflected effort saw him take the headlines, although he was keen to highlight the team effort.
The defence was particularly impressive at Stadionul Sheriff, where they held out for an 11th clean sheet from 14 matches.
"It is so important when the lads at the back are doing their job and keeping clean sheets," he said.
"It is just down to us to score because you know it is difficult to come to places like this win.
"But when you've got lads at the back that you know will can keep clean sheets, then we're confident we can go and win."
Only Southampton have a better defensive record in the Barclays Premier League - a record they will look to maintain on their return to domestic action on Sunday.
Hull are the visitors in a match that marks Tom Huddlestone's first return to the club.
The 26-year-old spent eight seasons at White Hart Lane but chose to leave in the summer in search of first-team football.
"We're all looking forward to seeing him," Defoe said of Huddlestone, who could play Spurs again in Hull's Capital One Cup tie in midweek.
"He was a great player here and is doing well for Hull, pulling strings and stuff.
"It is going to be a tough game but it is a game we have to win.
"It is important we keep winning football matches. I am looking forward to both games. We're a club that is going places."