Harry Kane and Raheem Sterling were also on target again as Gareth Southgate's men took their tally to 19 goals in four comprehensive wins in Group A.
Kosovo had been on a 15-game unbeaten run stretching back two years and were given the start to spark dreams of a monumental shock for a nation only given FIFA membership three years ago.
Just 35 seconds in, a misplaced pass by Michael Keane allowed Valon Berisha to fire past Jordan Pickford and give the visitors the lead.
England bounced back in emphatic fashion. It was another demonstration of the pace and firepower that will make the Three Lions among the favourites for Euro 2020 once the formality of mathematically securing their place at next summer's showpiece is out of the way.
The World Cup semi-finalists moved three points clear at the top of Group A ahead of the Czech Republic, who won, 3-0, in Montenegro. Kosovo dropped to third, four points behind. England have a game in hand on all four sides below them.
Sterling was in scintillating form, but the Manchester City winger scored his sixth goal in his last six international caps was in unusual fashion, with a towering header from close range.
For a half-hour spell England played football that sides far more experienced than Kosovo would have struggled to stop.
Sterling turned his marker and darted dangerously into the Kosovar half before teeing up Kane to drill low past Aro Muric. It was Kane's 26th international goal.
Sancho's low cross was then turned into his own net by Mergim Vojvoda and the Standard Liege right-back was further embarrassed as England struck twice more before half-time.
Sterling was too quick for the Kosovo defence as he cut in from the left before playing a perfectly weighted pass for Sancho to fire in at the near post for his first goal for his country.
A minute later, the 19-year-old had a second, again thanks to unselfish play from Sterling after leaving Vojvoda in his wake.
Yet, for all England's thrilling attacking play, there were concerns for Southgate over their defending as the hosts let Kosovo back into the game early in the second-half.
Berisha produced a second cool finish after Keane was caught under a cross from the right. Then Harry Maguire clumsily brought down Vedat Muriqi inside.
Muriqi dismissed Berisha's plea to take the spot-kick with the chance to complete a famous hat-trick and the Fenerbahce striker was relieved as Pickford just did not get a strong enough hand to save his penalty.
At the other end, Manchester City goalkeeper Muric produced some heroics as he saved Kane's powerful penalty. Then Sterling hit the post as England decided attack was the best form of defence with a two-goal cushion.
Muric also denied Marcus Rashford who had replaced Sancho, with a fine save. The Manchester United forward has a tough task to displace the Borussia Dortmund wonderkid in Southgate's first choice front three alongside Kane and Sterling.