The victory extended England's impressive run after their success against the Czech Republic in Prague and a commanding 7-0 win over Croatia. The latest result will have pleased Thomas Tuchel and the home supporters, with Kane once again at the centre of the action.
The England captain helped break the deadlock after 27 minutes when his cross was turned into the Czech Republic's own net by former West Ham United defender Vladimir Coufal.
Kane then doubled the advantage five minutes before half-time, finishing from close range after Morgan Rogers supplied an excellent first-time delivery.
The striker completed his brace in the 57th minute, heading Lewis Hall's corner into the net at the far post. His two goals took his international tally to 91, leaving him on course to become the first player to score 100 times for England.
The appearance was also a significant milestone for Kane, who drew level with Peter Shilton's record of 125 England caps.
Kane was withdrawn in the closing stages, with Dominic Calvert-Lewin coming on in his place. The Wembley crowd responded with a standing ovation as Kane left the field, capping an evening in which another landmark was added to his remarkable international career.
"I think it's necessary to move on. I think I can only repeat that we didn't go out on the group stage, sometimes it feels like that, but we didn't," Tuchel said after the win over Czech Republic, when asked about the World Cup semi-final defeat to Argentina.
"There was a bit of criticism and scepticism around, (but) I said we don't start new, I believe we don't have to start completely new because we can build on what we built together and we played some high-level competitive football in the World Cup.
"Now we move to the next step and it's always important to take the next step. But the commitment of the players and the attitude of the players from the first day in camp was on a very high level and I'm happy that we can prove it in all four matches."
