Manager Gareth Southgate kept Alli on for 80 minutes as he felt the midfielder was "still causing a problem" for Tunisia as England went in search of a victor - which eventually came in the 91st minute when Kane headed in his second.
Billy Grant, a Brentford fan from north London, said he was nervous about travelling to the World Cup host country amid fears of fan violence, racism in the stands and political tensions.
Harry Kane scored a dramatic late victor for England against Tunisia in the Three Lions' World Cup opener.
Kane has thrived under the management of Gareth Southgate, with his double in Volgograd taking his tally to 10 goals in eight internationals since Southgate took charge - including eight in six as captain.
Tunisia coach Nabil Maaloul said Kane was the difference between the two teams.
The 11 players chosen by Gareth Southgate had never all started an global together before - remarkably, it is the ninth consecutive World Cup in which that is the case for England. "He is the optimal striker", he said.
They found one in the form of a header from Harry Kane, whose uncanny ability to find himself in the right place at the right time once again pushed his team beyond the brink. The penalty was awarded after Kyle Walker caught Fakhreddine Ben Youssef with his arm. "We have dyed-in-the-wool supporters here, and we're looking to perform well for them".
Kane could not have asked for a more ideal start on an individual level, although England got lucky.
"There were a lot of decisions against us and maybe there was a bit of justice at the end".
After Belgium thrashed Panama 3-0 in the other Group G game on Monday, the pressure was on England to deliver only their second win in their last nine games at World Cups.
"We got told before that there was going to be a lot of flies and when we went out for the warm-up there were more than we thought".