Kane has scored just once in the Premier League for Tottenham Hotspur amid uncertainty about his future, but the Three Lions captain was irrepressible at Wembley.
The 28-year-old has scored 38 competitive goals in just 54 England games, more than any other player in English history, and has now moved level to the late, great Greaves on 44.
It was actually another Harry who opened the scoring, with Maguire heading home inside ten minutes after a delicious whipped free-kick from Reece James.
The Chelsea wing-back's display was described as 'nothing short of perfection' by Dean Ashton on commentary and he was waxing lyrical once again when James sent Jordan Henderson clear down his right hand side to cross for Kane's first.
Sensing a rout early on, Henderson then made the game safe inside a half hour after a one-two with Kane and some dancing feet more befitting of club teammate Mohamed Salah culminated in a left-footed finish.
Kane seemed to grow in confidence with every passing minute as he danced past the despairing Albanian tacklers to smash a left-footed finish just five minutes later, but he saved the best til last.
A wicked corner from the right-hand side by Ben Chilwell swerved past seemingly everyone in English blue, only for a spectacular Kane bicycle kick to send the ball shooting past Thomas Strakosha.
Gareth Southgate had sent out the most experienced England team from his five years in charge of the national side - with an average of 41 caps per man - and Ashton was loving it on talkSPORT.
"I've absolutely loved every single second of that," he said. "Best first half performance I have ever seen from England."
Kane is the first player in more than 100 years to score 10 goals in more than one calendar year for England and Spurs fans will have been relieved to see him withdrawn shortly after the break.
The experience levels quickly dropped as Southgate introduced a plethora of changes, including Arsenal's Emile Smith-Rowe for his senior international debut.
Naturally, the pattern of the game slowed to a pedestrian pace after all the changes and the fight had been drained from the visitors.
A point is all that is required on Monday evening against San Marino to ensure qualification for the World Cup in just over a year's time and, in this mood, England can afford to start booking their flights to Qatar.