Tottenham cut the Blues' lead at the top of the Premier League table to four points by thrashing Bournemouth 4-0 earlier today.
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.
"We expended a lot energy fighting against Leicester, but against West Brom, against Chelsea, against the media", Tottenham manager Mauricio Pochettino said, recalling last season's late costly draws against West Bromwich Albion and Chelsea.
Vincent Janssen capped off Spurs' afternoon by scoring just his second Premier League goal of the season in injury time, just minutes after coming on as a substitute.
Chelsea now travel to Old Trafford on Sunday afternoon knowing they can not afford to drop points with Pochettino's side ready to pounce should Antonio Conte's men slip up. Four points is still a lot. If they (Chelsea) drop points tomorrow that will be fantastic. "We fought against everyone, but now we are focusing on fighting our opponents when we play".
All Tottenham can do is keep racking up the wins - Saturday's was the seventh in a row - and raising the goal-difference advantage over Chelsea in case it matters. That levelled the record total for a South Korean player in a single European season, achieved by Cha Bum-Kun at German club Bayer Leverkusen in the 1985-86.
Moscow, Tehran, Damascus seek on-site probe into Syria gassing
The U.S. accuses the Syrian government of deliberately launching the deadly chemical attack in Khan Sheikhoun on April 4. Security Council and implies that the fate of Syria would be decided only by the Syrian people", he said.
Rafa Benitez bemoans added time decision as Leeds snatch late equaliser
When it was put to him that the game might have been stopped if it was a boxing match, he said: "We must have a granite chin". I will say again, if you analyse the last games , my understanding of the rules have changed a little bit.
People took my top-four finishes for granted - Wenger
Some have been making their feelings clear by protesting outside Arsenal's London Colney training base this week. Thus, we won't know for sure either way until Wednesday, but it really doesn't sound good.
Substitute Vincent Janssen rounded off the action with a fourth goal in stoppage time, the Dutchman's first Premier League strike from open play since joining past year.
The win sees Mauricio Pochettino's side set a new club record for consecutive league wins at home, 12, beating the previous benchmark set in 1922.
The Eagles were 2-0 down at home to Leicester, but launched a second-half comeback to rescue a point with goals from Yohan Cabaye and Christian Benteke.
James Collins restored West Ham's lead two minutes after half time, but Fabio Borini rescued a 90th-minute equaliser before Hammers defender Sam Byram was sent off in stoppage time.
It was his first goal since he made his return from a four-week lay-off with ankle ligament damage and left him three goals below Everton's Romelu Lukaku in the scoring chart.
Fellow relegation candidates Swansea and Hull also both lost.