The Three Lions had already secured top spot in the table but their latest victory ensured that Gareth Southgate’s side will be one of the top six seeds at the finals draw on November 30th.
Tottenham’s Harry Winks opening the scoring in Pristina, netting his first goal at international level on the half hour after beating three defenders before finding the bottom corner of the goal.
Sterling then turned provider as England registered a further three goals in the last 10 minutes.
First Kane fired home after Sterling’s cross was blocked and then looped up into the path of the England skipper who netted from close range.
Sterling then went on a superb run before putting in substitute Marcus Rashford who applied the finish and fellow sub Mason Mount then rounded off the victory in injury time with his first international strike.
Sterling’s City team mate John Stones was an unused substitute.
Meanwhile, Bernardo Silva provided an assist at Portugal secured a 2-0 win away at Luxembourg in Group B to secure their place at Euro 2020.
Bernardo's ball over the top had allowed Bruno Fernandes to fire the Portuguese ahead after 39 minutes.
And a second from Cristiano Ronaldo on 86 minutes sealed the deal and ensure that Portugal secured second spot in the table to book their ticket to next summer’s showpiece.
Joao Cancelo was an unused sub for the Portuguese.