The captain was in the right place early on to tap home and then netted again with a header in injury-time to earn a 2-1 win from the group G clash.
Gareth Southgate’s team were positive from the start and got an early reward.
Kane rolled the ball into the net on 11 minutes after a thumping header from John Stones was well saved.
Tunisia then had to substitute their keeper Mouez Hassen, who had started well, due to injury.
England continued to press on but missed some good opportunities.
They were soon harshly punished on 35 minutes when Kyle Walker was penalised for catching Syam Ben Youssef with his arm and the penalty was tucked away low by Ferjani Sassi.
Harry Kane should have had a penalty in reply but strangely a blatant rugby tackle in the area was ignored by the officials.
It was the same story in the early exchanges of the second half.
Kane was again dragged to the floor in the box but the referee was not interested.
It was surprising to see Kieran Trippier and Ashley Young on free-kicks as they both missed from good opportunities.
The match looked to be heading for a draw with Tunisia increasingly comfortable.
But in injury-time it was delight for England.
Trippier’s corner was headed on by Harry Maguire and Kane was left in space to guide his header into the net.
Meanwhile, Belgium crushed World Cup debutants Panama 3-0 in their group G opener in Sochi.
The Belgians dominated the opening 45 minutes but could not find a breakthrough as Panama goalkeeper Jaime Penedo kept them out.
Penedo clawed away an early effort from Dries Mertens before producing an even better save to deny Eden Hazard late in the half.
Belgium grabbed the lead two minutes into the second half with a fine strike from Mertens.
They extended their lead with a little over 20 minutes to go through Romelu Lukaku.
Kevin de Bruyne curled the ball with the outside of his right foot across goal for the striker to net with a diving header for 2-0.
Lukaku then made it 3-0 after Hazard’s pass.
Belgium play Tunisia on Saturday, June 23.
England’s next match is against Panama on Sunday, June 24.