Kane, who won the Golden Boot award last season with 25 goals as Tottenham challenged for the title, is only the fourth player since the start of the Premier League to score 20 goals in three successive seasons - joining Thierry Henry, Alan Shearer and Ruud van Nistelrooy.
The 23-year-old still has a long way to go to match the exploits of Greaves, but his goals are helping Tottenham stay in touch with leaders Chelsea as they try to win the English title since 1961 when Greaves was in his pomp.
Kane played down his feat, insisting the only focus was on Tottenham maintaining the form that has seen them win seven consecutive top-flight games for the first time in 50 years.
"It's good to be consistent as a striker. I want to do that year in year out. We've still got plenty to do this season so I don't want to think about it," Kane said of his achievement. "Hopefully, Manchester United can get a result tomorrow and do us a favour."
Manchester City kept pace to move into third place and remain seven points behind Spurs with a 3-0 win over Southampton.
Vincent Kompany scored his first goal in 20 months in only his second start on his latest comeback from injury for City when he opened the scoring in the 55th minute.
Leroy Sane grabbed a second in the 77th minute moments before Sergio Aguero chipped in with his 29th goal of the season - and 11th in 11 games - to seal a comfortable victory.
At the opposite end of the table Sunderland very nearly pulled of a much-needed late comeback against 10-man West Ham but had to settle for a 2-2 draw which will almost certainly seal their relegation.
The Black Cats twice came from behind to level things Wahbi Khazri scoring from a corner to cancel out Andre Ayew's opener before Fabio Borini levelled again on 90 minutes after James Collins had again put West Ham ahead on 47 minutes.
Resurgent Crystal Palace pulled off a similar feat at Selhurst Park, coming from 2-0 down to draw with Leicester and put themselves seven points above the drop zone.
Robert Huth and Jamie Vardy had both scored to give Leicester a 2-0 lead after 54 minutes but a 54th minute strike for Yohan Cabaye and a 70th minute Christian Benteke header made it 2-2 at fulltime.
Fellow relegation candidates Swansea and Hull also both lost.
Swansea fell 1-0 to Watford to stay in the drop zone when Etienne Capoue scored the only goal of the game in the 42nd minute.
Gylfi Sigurdsson missed two late chances to equalise, heading just wide before running through and then failing to get enough power behind a shot.
Hull were humbled 3-1 at Stoke City in a game where they squandered several first half chances.
Stoke led 1-0 at the break but Hull started the second half well and Harry Maguire levelled things in the 51st minute before Stoke again took the ascendancy. Late goals to Peter Crouch and Xherdan Shaqiri sealed the result.
Everton also recorded a 3-1 win over Burnley with Phil Jagielka and Romelu Lukaku scoring and Ben Mee netting an own goal.
