A minute later, the 19-year-old had a second, again thanks to unselfish play from Sterling after leaving Vojvoda in his wake.
“I’m delighted to score my first goal for England,” said Sancho.
“It was a crazy game. Five goals and I’m just happy to get two of them.”
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.
Maguire, the world’s most expensive defender after an £80 million move from Leicester to Manchester United last month, then clumsily brought down Vedat Muriqi inside the area.
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 and only the post denied Sterling a sixth, but England had already done enough to move another step closer to Euro 2020.