Kane got England out of jail with an injury-time winner at the Volgograd Arena to ensure Gareth Southgate's side claimed all three points from their opening Group G game.
England had almost paid a heavy price for missing a slew of first-half chances when Tunisia's Ferjani Sassi slotted home a softly-awarded penalty 20 minutes before half-time.
And the north Africans were still level as the game went past the 90-minute mark.
But Harry Maguire won a header from a corner and Kane was on hand at the far post to nod in the winner before being mobbed by his ecstatic teammates.
"I'm so proud of the lads," Kane said. "They kept going, kept going to the last second. I am absolutely buzzing, everyone on the staff is. It shows good character to get the job done."
However Kane admitted he was frustrated by several decisions from referee Wilmar Roldan, who ignored several incidents involving Tunisian defenders tangling with the England captain.
One first half collision which saw Sassi wrestle Kane to the ground in the penalty area was widely replayed across social media after the game.
"I was maybe a bit disappointed by that," Kane said. "I guess that's what VAR is there for, to look at them decisions. If they don't think that was a penalty, we have to deal with that.
"For me, I struggled to get them off me. I tried to run at a few corners and couldn't move. I guess as players there's nothing we can do about that. We just have to hope the officials get it right more often than not."
England had started brightly in a blur of passing and movement and could have been two goals up inside the first four minutes.
First Jordan Henderson's lofted first-time pass released Dele Alli and when the ball eventually broke to Jesse Lingard he saw his shot from six yards saved by the outstretched left boot of Mouez Hassen in the Tunisia goal.
Kane had been kept quiet in the opening salvos but he exploded into action in the 11th minute when he cut inside from the left and saw his shot from the edge of the box deflected wide for a corner.
Ashley Young delivered the set piece for John Stones to rise highest and meet with a powerful header. Hassen saved acrobatically but Kane was on hand to tap home the rebound with his right foot and open his World Cup account.
Hassen, who had injured his left shoulder making an earlier save, could not continue and left the field in tears as he was replaced in goal by Farouk Ben Mustapha.
England continued to press and were made to pay for not converting a succession of chances when they conceded their penalty.
Kyle Walker swung a lazy arm across Fakhreddine Ben Youssef who fell as if poleaxed and Colombian referee Wilmar Roldan pointed to the spot, with his decision being upheld by the VAR.
jpegMpeg4-1280x720Ferjani Sassi took one step and fired home confidently past the hitherto unemployed Jordan Pickford and Tunisia who had been outplayed for the first half-hour were somehow level 10 minutes before half-time.
Still there was time for Lingard to come close again twice, first from a goalbound shot and then a dink over the keeper which agonisingly struck the post.
Alli too hit the woodwork with a header and England went into half-time wondering how they had not sealed victory already.
England still enjoyed the lion's share of possession but could not find the same zip and penetration they had enjoyed at the start of the first half.
The ineffective Sterling gave way to Marcus Rashford with just over 20 minutes to go and the Manchester United man almost fashioned a chance straight away with a jinking run into the box.