Kane had scans on Wednesday but England manager Southgate said there was no serious damage.
Two goals from Bukayo Saka and strikes by Jude Bellingham, Raheem Sterlinga, Marcus Rashford and Jack Grealish rounded off the rout.
Five different players scored for England with Bukayo Saka bagging a brace. Mehdi Taremi hit both of Iran's goals.
The FIFA World Cup is the biggest test for a footballer and greatness is attained based on the heroics in the showpiece.
The England captain also missed a penalty in the 2-0 win for Antonio Conte's side.
The Arsenal captain scored twice in a solid 3-0 win to move to top of the table.
Chelsea manager Thomas Tuchel and his Spurs counterpart Antonio Conte were both shown red cards after the final whistle as tempers boiled over on a sweltering afternoon in west London.
Dominik Szoboszlai earned Hungary a shock 1-0 win over England.
Among the others involved in the series are soccer's Pep Guardiola and Harry Kane, multiple Olympic swimming champion Michael Phelps, boxers Canelo Alvarez and Oscar De La Hoya as well as American football's Ben Roethlisberger.
A mistake by Liverpool keeper Alisson gifted Tottenham's Son Heung-min a 74th-minute equaliser the hosts fully deserved although the visitors were fuming about some contentious decisions.