Kane headed home from Christian Eriksen's corner in the 89th minute to make up for two glaring misses earlier in the match at Selhurst Park.
Sheffield United pulled off the first major shock of FA Cup third round weekend when the third-tier English side triumphed 3-0 at Premier League outfit Queens Park Rangers on Sunday.
Zlatan Ibrahimovic was again at his irrepressible best with another double earning Jose Mourinho's increasingly confident Manchester United a 2-0 win at West Bromwich Albion in the Premier League on Saturday.
The battle to avoid relegation is now a straight shootout between Hull City and 17th-place Newcastle United, who are two points better off heading into Sunday's final round.
Patrik Schick scored his fourth goal of the tournament as the Czech Republic stunned 10-man Netherlands
Chelsea are now 11 points ahead of Manchester City who have 13 games left to play and while Italian Conte is too cagey to start proclaiming his side yet, only a monumental loss of form can deny them the title.
Everton have 36 points from 26 games
Spurs striker Bergwijn is major casualty as Netherlands trim squad
Leicester City were left in touching distance of a fairytale first Premier League title on Sunday after Leonardo Ulloa's double helped them outclass Swansea City at a delirious King Power Stadium.
Second-half goals from Willian and Diego Costa helped Chelsea ease past Hull City 2-0 on Saturday and grab their first win in four Premier League games.
Manchester United kept up their chase for a Champions League qualification spot with Marcus Rashford and Anthony Martial on target in a 2-0 Premier League win over Crystal Palace, while Leicester secured a 2-0 home win over Sheffield United.
Manchester City produced a blistering first-half performance to win 4-1 at Sunderland in the League Cup third round on Tuesday, inflicting more misery on Dick Advocaat's struggling side.
Leicester City's Premier League title defence got off to a terrible start as they were beaten 2-1 at promoted Hull City, who shrugged off an injury crisis to shock the champions on the opening day of the new season on Saturday
Swansea City's hopes of salvaging their place in the Premier League suffered a potentially grievous blow as Ryan Fraser's deflected strike earned Bournemouth a 1-0 win on Saturday to secure another season of top-flight football for the Cherries.
IMAGES from the English Premier League match played at Selhurst Park in London on Monday
It was a third successive 0-0 draw for United after a stalemate at Chelsea on Sunday and against Real Sociedad last Thursday which completed a 4-0 aggregate win over the Spanish side in the Europa League.
Liverpool made it three wins out of three as Mohamed Salah scored twice in a convincing 3-1 victory over Arsenal on Saturday to take control at the top of the Premier League.
News of all that tranpired on and off the football field.
Photos from the English Premier League matches played on Sunday
IMAGES from the EPL matches played on Sunday.
Christian Benteke headed home from close range as Liverpool grabbed a stoppage-time leveller to snatch a point against Chelsea in a 1-1 draw on Wednesday after Eden Hazard's dazzling opener for the visitors.
Aston Villa were relegated from the Premier League for the first time since it began in 1992 when they suffered their 24th loss of the season in a 1-0 defeat at Old Trafford on Saturday.
Chelsea maintained their stranglehold on the Premier League by beating Sunderland 1-0 on Wednesday to register their 10th successive win and move six points clear at the top of the table.
Normally the candidates for goal of the season are spread throughout the 10 months of the campaign, but this weekend's Premier League matches produced six memorable strikes in little over 24 hours.
Jermain Defoe made himself an instant Sunderland hero with a sensational volleyed goal to seal a vital 1-0 win over North East rivals Newcastle United in the Premier League on Sunday.
McTominay injury takes gloss of vibrant United display
Sunderland striker Steven Fletcher scored in each half to help his beleaguered side earn a much-needed 3-1 win at Crystal Palace in their Premier League match at Selhurst Park on Monday.
The victory takes Pep Guardiola's side into provisional second spot
Cesc Fabregas and Branislav Ivanovic struck late goals to earn improving champions Chelsea a 2-1 victory at Southampton in the Premier League on Saturday.
Photos from the English Premier League matches played on Saturday
Leaders Chelsea stretched their Premier League winning run to a club record-equalling 11 as Diego Costa's header shortly before halftime secured a 1-0 victory at London rivals Crystal Palace on Saturday.
IMAGES from soccer matches played in the EPL, La Liga and Serie A on Tuesday.
Under-pressure Everton manager Roberto Martinez enjoyed some respite as his struggling side won for the first time in eight league matches.
News of all that's transpired on and off the football field
With Liverpool still to visit Chelsea, who trail them by nine points with two games in hand, Juergen Klopp's side may have to beat Brighton & Hove Albion on May 13 and rely on their superior goal difference to qualify for the Champions League, assuming they do not secure it by winning this year's trophy.
Liverpool substitute Adam Lallana struck deep into stoppage time to snatch a 5-4 win over shell-shocked Norwich City in an extraordinary Premier League game at Carrow Road on Saturday.
Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
An insatiable Lionel Messi scored for the eighth game in a row in all competitions as La Liga champions Barcelona saw off a gutsy Girona side 2-0 to go five points clear at the top of the standings.
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