Kane, now the league’s leading scorer, became only the fifth Englishman to net 20 Premier League goals in consecutive seasons as his double and a Christian Eriksen strike secured a comprehensive victory over Bournemouth.
Spurs trail leaders Leicester by five points with seven games remaining and now look like the only side capable of catching Claudio Ranieri’s team.
Pochettino’s men face tricky fixtures against Liverpool and Manchester United after the international break but the Argentine insisted neither he or his players are concerned by their tough run-in.
“We cannot change the fixtures, every circumstance is different,” said Pochettino.
“We’re in a position we deserve to stay in and now we have to reduce the gap.
“Leicester have a good advantage. We need to fight and believe. The most important thing is never to give up.”
With the Europa League no longer a distraction, Pochettino was able to name a strong lineup as he welcomed back Kane, Eriksen, and Mousa Dembele, who were all rested for Thursday night’s defeat to Borussia Dortmund.
Only Spurs and Leicester have bagged more points than Bournemouth since the start of December and Eddie Howe’s buoyant side arrived at White Hart Lane with the chance to surpass the magic 40-point mark and put to bed any lingering doubts about their Premier League status.
Leicester’s win over Palace on Saturday meant there was no room for error for Tottenham and they quickly dispelled any tension in the stands by taking the lead after just 44 seconds.
Hugo Lloris spotted Kyle Walker in space and the full-back was given the freedom of the right flank to pick out Kanewith a fizzed cross and the forward managed to get a faint touch on the delivery to divert past Artur Boruc.
Now brimming with confidence, the hosts piled forward in search of a second and it duly arrived in the 16th minute via a familiar combination.
After some patient build-up play, Dele Alli was found in a pocket of space and instantly played in Kane with a slide-rule pass. The league’s top marksman never looked like missing as he coolly slotted into the bottom corner.
Seven of Kane’s 21 goals this season have now been provided by Alli, and Tottenham’s title hopes will heavily rely on the pair continuing their prolific understanding.
“I think Harry is one of the best strikers in the world. His performance was fantastic,” said Pochettino.
Clearly shellshocked by the constant waves of Tottenham attacks, Bournemouth’s ventures outside their own half were few and far between. Their solitary effort on goal in the first half came in the 41st minute when Steven Cook headed over Max Gradel’s inswinging free-kick.
Howe made two changes at half-time in an attempt to find a way back into the game, with the ineffective Benik Afobe replaced by Lewis Grabban, while Harry Arter made way for fellow Irish midfielder Eunan O’Kane.
Bournemouth did improve for a brief period after the break, forcing a string of corners, but Tottenham remained in cruise control and secured the points six minutes into the second half.
Kane found himself in space 25 yards from goal and didn’t need a second invitation to let fly. His fierce shot could only be parried by Boruc and Eriksen was on hand to convert a simple tap-in.
Although Tottenham will face sterner tests in their final seven games of the season, Pochettino was encouraged by how fresh his side looked.
“The energy of the team was fantastic. When you come out of a very busy like we have, I think you can feel very proud because we showed a lot of maturity,” he added.
For all their fluidity and invention going forward, it was also another supremely assured display from Tottenham’s back four with centre-back pairing Toby Alderweireld and Kevin Wimmer rarely troubled.
Spurs should have added a fourth in the closing stages. Eriksen wriggled into some space after he exquisitely turned past Charlie Daniels and squared for Alli but the midfielder miscued wide.
“Tottenham moved the ball very well and we didn’t execute our game plan,” said Howe.
“They make the pitch very big and stretch you. They switch the ball very well and then you’ve got the quality of Kane up front. When he gets time he hurts you.”
Lloris 6, Walker 7, Alderweireld 7, Wimmer 7, Rose 8, Dembele 7, Dier 7 (Chadli 89), Eriksen 8 7, Lamela 6 (Carroll 66 5), Alli 7 (Mason 81), Kane 9
Vorm, Tripier, Walker-Peters, Son,
Boruc 4, Smith 5, Francis 4, Cook 5, Daniels 4, Surman 5, Arter 5 (O’Kane 46 5), Ritchie 6, Gradel 6, King 5, Afobe 3 (Grabban 46 5)
Federici, Gosling, Elphick, Pugh, Distin,