Before that goal, a Kyle Walker mistake led to a one-on-one, saved by Jordan Pickford, and visitors to Wembley did not come close to scoring again.
Jordan Henderson made it 3-0 before half-an-hour was up when England cut through the middle of the Albanian defence. A flying save prevented Kane making it 4-0 soon after but the England captain did just that with another couple of minutes played, a left-footed finished from that side of the goal.
Kane was just wide with a couple of hat-trick chances before the interval, the second from a James cross, but on the verge of the half-time whistle he volleyed in a corner to make it 5-0.
Midway through the second half, there was a clash of heads between James and John Stones which floored both players. After treatment, they continued and the Chelsea man shot wide with his next involvement but not that long after he was withdrawn.
Chilwell played the whole game and although less prominent as an attacking force than his club colleague, he put in a tidy display and was rarely tested in his defensive work.