That shaky rearguard creaked again moments later as Rrahmani found himself in acres of space but headed woefully wide with the goal at his mercy.
England’s class told in the second half and Kane hit the post with a snap-shot from Sterling’s pass.
The same pair linked up for a milestone second goal in the 79th minute.
Sterling eased past his marker and sent in a deflected cross that England captain Kane finished off at the far post.
Kane has netted in all eight qualifiers and is the first England player for over 90 years to score 12 international goals in a calendar year.
It was also England’s 35th goal of the qualifying campaign, breaking their previous record total from the 2010 World Cup qualifiers.
There was still time for Rashford to slot home from Sterling’s pass in the 83rd minute before Mount took Kane’s delivery and coolly finished in stoppage time.