Christian Eriksen's late winner sent Tottenham within two points of the Premier League summit on Sunday, his calm finish earning a 2-1 win over title rivals Manchester City at the Etihad Stadium.
Spurs slipped from second thanks to Arsenal's 2-1 win over leaders Leicester City earlier in the day, but Kane's spot-kick, following a questionable handball call against Raheem Sterling, looked to have taken the visitors back above their London rivals.
City - beaten 3-1 by Leicester at the Etihad eight days ago - were level in the 74th minute courtesy of substitute Kelechi Iheanacho shortly after the 19-year-old's introduction from the bench as Manuel Pellegini's men looked to have kept their title hopes alive.
However, it was Eriksen - celebrating his 24th birthday - who had the final say, slotting home Erik Lamela's pass amid lacklustre City defending on captain Vincent Kompany's return from injury.
A second defeat of the season to Spurs, alongside losses against Arsenal and Leicester, look set to prove costly for the outgoing Pellegrini, who saw David Silva go agonisingly close late on, while Mauricio Pochettino's men have now won five top-flight games on the bounce.
While City called on influential skipper Kompany, Pochettino brought in Kyle Walker and Danny Rose at full-back, with Dele Alli returning to the XI after suffering dizziness in the win against Norwich City.
Son Heung-min was also recalled to the line-up and, after Sergio Aguero turned an awkward effort over the crossbar 10 minutes in, the South Korean was denied an opening goal by an offside flag.
Silva, who shook off an ankle knock to play, saw a dangerous strike deflected wide, while Rose bravely blocked Sterling's volley before the half-hour mark.
Eriksen stung Joe Hart's palms soon after, but neither side could break the deadlock in a closely contested first period.
Aguero almost caught Spurs napping early in the second half when he sent Kolo Toure's blocked cross high over the crossbar from close range before Spurs were given a helping hand in taking the lead.
Sterling was harshly adjudged by referee Mark Clattenburg to have handled Rose's cross, allowing Kane to tuck home the opener eight minutes into the second half amid jeers from an angry Etihad crowd.
The hosts set about restoring parity as Fernandinho headed Silva's corner over the crossbar before Toure rattled the woodwork with a free-kick from just outside the area.
Pellegrini then threw caution to the wind as Iheanacho replaced Fernando after the hour and it took little time for the Nigerian to make an impact with his ninth City goal in all competitions.
The 19-year-old kept a cool head and calmly side-footed Gael Clichy's cross past a helpless Hugo Lloris 16 minutes from time, only for Eriksen to take advantage of sloppy defending from City to settle the contest in Spurs' favour.
Lamela's ball dissected the City defence and birthday boy Eriksen coolly registered the winner, although Spurs were forced to withstand heavy pressure late on as Silva could only shin an effort over the crossbar from point-blank range to compound City's frustration.
Key Opta Stats:
- Manchester City have won just one of their 10 Premier League games against sides currently in the top eight this season (D3 L6).
- Tottenham ended a run of five successive league defeats at the Etihad Stadium, earning their first victory there since May 2010.
- Harry Kane has scored 15 goals in his last 17 Premier League games.
- Since the start of last season, only Sergio Aguero (40) has scored more Premier League goals than Kane (37).
- Tottenham have won five consecutive Premier League games for the first time since a run of six in December 2011.