Ferjani Sassi scored the resulting spot-kick and Tunisia were able to keep England at bay until the dying moments.
However, missed chances from Jesse Lingard, who was guilty of wasting a number of opportunities, and Dele Alli meant that England's lead remained slender.
Hopes for England were quietly growing before the Tunisia clash, with Gareth Southgate's side earning some praise for having a more understated approach than previous squads, but the end product was all too familiar.
Tunisia coach Nabil Maaloul selected striker Wahbi Khazri for his first match since April after an injury and wingback Ali Maaloul also plays despite picking up a muscle strain in a friendly against Spain earlier this month. "I thought we played well, especially in the first half". John Stones met Ashley Young's corner with a great header, and even though goalkeeper Hassen made an excellent save to claw it out the ball fell to the feet of Kane who slotted home from just three yards out. The penalty was awarded after Kyle Walker caught Fakhreddine Ben Youssef with his arm.
Marcus Rashford replaced the ineffectual Raheem Sterling with 20 minutes remaining but still England struggled to create.
England begins their 2018 FIFA World Cup run today against Tunisia as the third and final soccer game on today's schedule.
Not since Germany 2006, when Sven-Goran Eriksson's team claimed a narrow 1-0 win against Paraguay in Frankfurt, have England got off to a flier in a World Cup, and this was only the sixth time they have managed it in 15 attempts. I feel very happy for the England boys because if they hadn't have gotten there, the next couple of days would have been awful for them.
Euro 2016 ended in humiliation for Kane and England with a loss to Iceland in the last 16, but the team has been transformed by Southgate.
'We've done for a while since gaffer has been here, good togetherness, ' he said.