England's talisman and captain put them ahead in the 11th minute of Monday's clash in Volgograd, but Tunisia levelled in contentious fashion.
Referee Wilmar Roldan pointed to the spot when Kyle Walker caught Fakhreddine Ben Youssef with his arm and Ferjani Sassi levelled with an unconvincing penalty.
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.
Gareth Southgate's men appeared to run out of ideas in the second half, with Tunisia seemingly set to see out what would have been an unexpected draw.
But in the first minute of injury time they made the mistake of leaving Kane unmarked in the box for the second time and he took advantage by heading home at the far post to ensure England start the tournament with a deserved, if unconvincing, win.
Jesse Lingard would have opened the scoring in the third minute had Mouez Hassen not pulled off a fine save with his legs after the Manchester United forward was found by a cutback from Dele Alli.
Hassen appeared to suffer an injury when he collided with Lingard as he raced clear down the left and squared for Raheem Sterling, who will have taken comfort from an offside flag after a glaring miss.
The knock did not stop the Tunisia keeper producing heroics to keep out John Stones' header, but he could do nothing about the follow-up as Kane confidently tucked home.
Hassen was withdrawn four minutes later for Farouk Ben Mustapha, who was tested by a long-range drive from Jordan Henderson, with Lingard then spurning a gilt-edged chance as he mishit a volley from Ashley Young's cross to the far post.
And 10 minutes before half-time England were punished for wasting chances as Roldan ruled Walker had intentionally made contact with Ben Youssef, Sassi's penalty powerful enough to beat the fingertips of Jordan Pickford and find the bottom-left corner.
England had a legitimate case for a spot-kick at the other end when Kane was bundled over in the box as Alli headed against the crossbar.
Southgate's men will have been frustrated by their profligacy, Lingard latching on to a ball over the top and knocking it past Ben Mustapha, only to see it trickle onto the post and wide.
Kane had another appeal for a penalty waved away within five minutes of the restart as he was impeded by a pair of Tunisia players at a corner, but the rate at which England appeared to run out of gas was alarming.
Young drifted a free-kick well over the bar and England's chance at victory appeared to have gone.
However, Harry Maguire flicked a Kieran Trippier delivery into the path of Kane, who made no mistake from point-blank range to break Tunisian hearts.
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