With Sunday's 2-0 loss to Arsenal, Everton have now conceded two goals in each of their three away games this term.
Kane was under the spotlight after going five games without a goal for club and country, but he scored a first-half penalty to end his mini-drought.
Manchester United were held by Wolves at Old Trafford and Paul Pogba said they had not been able to create enough chances to win the game.
No team has successfully defended the Premier League title for 10 years but Pep Guardiola has targeted domestic superiority.
Alexandre Lacazette and Pierre-Emerick Aubameyang were Arsenal's match-winners against Everton but Petr Cech was the star man, earning 8/10.
Arsenal's defence was bailed out by the under-pressure Petr Cech, and a pair of goals three minutes apart secured the Gunners a win over Everton.
Alexandre Lacazette broke the deadlock before Pierre-Emerick Aubameyang -- in an offside position not seen by the officials -- grabbed the second.
Olivier Giroud's telepathic understanding with Eden Hazard went missing as Chelsea's attack misfired in a scoreless draw at West Ham on Sunday.
Chelsea manager Maurizio Sarri refused to use Europa League fatigue as an excuse after his team was held to a goalless draw at West Ham.
Maurizio Sarri's side suffered an afternoon of frustration but could easily have lost, Andriy Yarmolenko nodding a great chance wide.
|Brighton & Hove Albion||6||1||2||3||-3||5|
|West Ham United||6||1||1||4||-6||4|