The starting XI named by manager Gareth Southgate for the landmark match was the youngest England team since 1959 with an average age of 23 years and 255 days.
However, Raheem Sterling was not involved as punishment for his part in a spat with Joe Gomez on Monday, with Southgate opting to play Borussia Dortmund forward Jadon Sancho in his place.
There was also a first England start since March 2018 for Liverpool midfielder Alex Oxlade-Chamberlain and he opened the scoring.
Kane netted two of his three goals before Marcus Rashford got his name on the scoresheet.
Kane completed his treble and scored England's fifth after 37 minutes as England's 289th match at Wembley turned into a procession.
The strike saw Kane become England's highest-ever goalscoring captain as he celebrated a 24th goal while wearing the armband.
It was the perfect 45 minutes of football to precede the on-field commemoration of England's 1000th game.
A video montage of memorable moments was followed by a host of former internationals making their way onto the pitch.
The likes of all-time leading goalscorer Wayne Rooney and former captain Tony Adams were joined by the likes of Sol Campbell, Paul Gascoigne, David Seaman, Des Walker and Martin Keown.
It took England until the 66th minute to add to their tally when Aleksandar Sofranac scored an own goal, before Gomez was introduced from the bench.
Another substitute, Tammy Abraham, sealed England's biggest win at the new Wembley by rounding off the evening's scoring with his first international goal.