England wasted numerous opportunities prior to that leveller but will have been unimpressed by Roldan's performance thereafter, the Colombian ignoring multiple penalty appeals from the Three Lions.
And the captain's last-gasp victor after Ferjani Sassi had equalised with a dubious penalty sparked frantic scenes of celebration as England got their World Cup campaign off to a winning start.
The winning goal came at the end of a drab second half in which Tunisia defended deep and nullified England's attack.
But Harry Maguire won a header from a corner and Kane was on hand at the far post to nod in the victor before being mobbed by his ecstatic teammates. Despite being thoroughly outplayed, Ferjani Sassi's penalty sent Tunisia in at the break level.
'We've done for a while since gaffer has been here, good togetherness, ' he said.
'We've got this result over the past few weeks and that's because of everyone.
Belgium's stars come out to shine in 2nd half against Panama
Sweden and South Korea get things underway today, and with Germany suffering defeat to Mexico on Sunday, Group E is wide open. The Swedes later advanced by eliminating Italy in a play-off.
'Everyone, all the staff included, will be delighted and we'll get on that plane happy tonight'.
England had started brightly in a blur of passing and movement and could have been two goals up inside the first four minutes. I'm so proud of the lads.
"The first half we should have been clear". The former English captain insisted that he could not be talked out of his decision to not play in the World Cup.
"It's a massive boost, a massive bonus, we kept going".
The North Africans were level in the 34th minute when Kyle Walker caught Ben Youssef with his arm on a cross and the referee pointed to the penalty spot.
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.