Spurs are now just two points behind leaders Leicester City, who play Newcastle on Monday night, and the win at Villa Park took them six clear of north London rivals Arsenal in third.
Manchester City and Arsenal’s challenges have laboured in recent weeks, paving the way for Leicester and Tottenham to emerge as the two main contenders, but Pochettino insists the title race still remains wide open.
“We’re in a good position but there’s a lot of games to play,” said Pochettino.
“We’ll see what happens but it’s too early to put some teams out of the race.
“We are in the race and if you compare last season with this season we need to feel proud of our players.
“Our supporters are right to dream and we need to dream but keep working hard.”
Pochettino made seven changes to the inexperienced line-up he fielded against Dortmund, with the key quartet of Kane, Dele Alli, Eric Dier and Mousa Dembele all restored.
As a result, Spurs looked fresh and reenergised from the off and they should have been ahead inside four minutes.
Erik Lamela carved open Villa’s defence with a slide-rule pass to find Kane but the forward was forced into an improvised chip by the on-rushing Brad Guzan and his effort rattled the bar.
Apart from sporadic Villa breaks forward, Pochettino’s side controlled proceedings in the first half and wasted several chances before they eventually broke the deadlock on the stroke of half-time.
In the 24th minute Danny Rose picked out Kane with a low cross but Guzan did well to get across his goal and parry away.
The American goalkeeper has been on the end of his fair share of criticism from Villa fans this year but they had him to thank for remaining level for the majority of the half.
He was once again quick off his line to foil Kane before showing sublime reflexes to tip Lamela’s attempt onto the post.
But just as Guzan and Villa thought they had made it to the break on terms with a far superior Spurs, they were hit by a sucker-punch courtesy of quick-thinking from Alli and Kane.
Alli was fouled midway inside the Villa half and immediately picked himself up and spotted the run of Kane with a clipped free-kick. This time the man in the mask made no mistake, shooting across Guzan and into the corner.
The second goal was a thing of beauty - with Alli and Kane again combining - and demonstrated why Tottenham have the quality to overhaul Leicester and claim a maiden Premier League crown this season.
Lamela robbed Carles Gil of possession in midfield and rolled the ball out to Alli, who waited for Kane to take up his position in the six-yard box before squaring for the striker to tap in his second and increase his league tally to 19 goals this term.
Not for the first time this season, Villa fans then directed their frustrations towards owner Randy Lerner and chief executive Tom Fox with repeated chants calling for their heads.
When asked about the protests, Garde said: “Nobody has to forget what happened in the past and what has been done in the past by everybody involved in this football club.”
The home side’s afternoon and season was summed up by two glaring misses late on. First, Rudy Gestede rattled the bar from three yards out before Joleon Lescott somehow volleyed wide at the back post from the forward’s flick-on.
Guzan 6, Hutton 5, Okore 4, Lescott 4, Cissokho 3, Westwood 4, Gana 5, Ayew 5, Gil 4 (Sinclair 69), Veretout 4 (Green 62 4), Gestede 5
Bunn, Richards, Clark, Bacuna, Lyden
Lloris 6, Walker 7, Alderweireld 7, Wimmer 7, Rose 7, Dier 6, Alli 8 (Mason 86), Lamela 7 (Chadli 90), Dembele 6, Eriksen 7 (Carroll 77), Kane 8
Vorm, Trippier, Davies, Son