England now face Panama on Sunday, with a win or a draw likely to secure a place in the knockout stages.
"I know Southgate is a massive fan of Sterling but I think he would be quite within his rights to drop him for the Panama game".
Tunisia coach Nabil Maaloul said he didn't feel them because he was "so focused on the team, on the game".
The Tottenham star followed up a John Stones header that was initially saved by Tunisian keeper Hassan. Not the hardest one to score in his career, but surely one of the most important.
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.
Alli played 80 minutes of last night's 2-1 Group G victory in Volgograd, despite Fabian Delph being stripped and seemingly ready to come on in the first half.
On every set piece, he was rugby-tackled by Tunisia defenders but Wilmar Roldan, the Colombian referee, never said anything.More news: United States 'to announce withdrawal from UN human rights council'
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Twice in the first half, Kane was restrained by Tunisia defenders on a pair of corners only for Colombian referee Wilmar Roldan to wave play on, so the Tottenham striker thought it was only fair that he get the chance to score the victor.
Finally, they got their goal. He found himself more isolated against three physical centre-backs, muscled out too often by Dylan Bronn, a right-back from Gent, Syam Ben Youssef, a regular at Kasimpasa in Turkey, or Yassine Meriah, who has played his entire career in his native Tunisia.
"The crucial thing is taking the chances in this tournament. These are not half chances, these are very, very good chances that we should be putting in the back of the net".
England felt they could have had two penalties as Kane was man-handled in the box by the Tunisian defenders, with the Tottenham striker suggesting his late victor was just reward after a dubious refereeing performance.
He said: "Credit to the lads, we kept going".
With the north Africans happy to take a 1-1 result, England looked as if they were going to pay for their lack of composure as the minutes ticked away. "We got lucky and we got the goal in the end". Each time, it is just about getting Kane to the floor. Trippier's delivery was headed on to the unmarked Kane at the far post, and he made no mistake with a fine close-range header.
A visibly delighted England manager Gareth Southgate said after the game: "Good teams score late".
The English have brought one of their weakest squads in a long time to the World Cup, which has decreased the expectations placed on the Three Lions.