Tottenham cut the Blues' lead at the top of the Premier League table to four points by thrashing Bournemouth 4-0 earlier today.
It was also a good afternoon for misfit striker Vincent Janssen - who netted only his second Premier League goal and his first from open play - as he scored the fourth of Tottenham's goals, which led to a passionate celebration from his manager.
"It was important for us to get the three points and we got the three points", Pochettino said.
A quick-fire double from Dembele and Son put them in command, and Kane made it safe just after the break to send them on the way to another comprehensive win at home, while it was their seventh straight league victory, something they haven't achieved in 50 years.
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Victory narrowed the gap to four points ahead of Chelsea's tricky-looking trip to Manchester United on Sunday.
Bournemouth are now without a win in four matches and remain seven points above the bottom three.
It was nearly the ideal game for Spurs as it witnessed, four goals, a clean sheet, no injuries and even the heartwarming sight of substitute Vincent Janssen scoring his first ever Premier League goal from open play. We are fighting for ourselves to be there. We've still got plenty to do this season so I don't want to think about it.
Bournemouth began to enjoy their best spell of the game after going two down, much to the frustration of Pochettino on the sideline.
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Mousa Dembele scored his first goal of the season, Harry Kane reached 20 goals for a third successive season and striker Vincent Jansson netted his first from open play in the league since joining Tottenham previous year. It's the third successive year that Kane has hit 20 league goals in a season. Leicester has mounted a feeble defense of its title - sitting 12th - but it is England's last Champions League participant and hosts Atletico Madrid on Tuesday in the quarterfinals.
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.
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.
Premier League top scorer Romelu Lukaku struck Everton's third, taking his season tally to 24.
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After Borini's late leveler, West Ham finished with 10 men after Sam Byram was dismissed in the fifth minute of stoppage time after being shown a second yellow card.