England took the lead in the 70th minute when substitute Alex Oxlade-Chamberlain's left-foot strike beat goalkeeper Craig Gordon's flimsy attempt at a save.
But Kane stunned the crowd two minutes into injury time when he volleyed home a ideal pass from Raheem Sterling, a goal that prevented what would have been England's first World Cup qualifying loss since a defeat to Ukraine in 2009.
England manager Gareth Southgate insists England's injury-time equaliser against Scotland is a "big moment" for the team, as they finally proved they have character.
Scotland can still qualify for the World Cup finals in Russian Federation, despite the "bitter disappointment" of conceding a late equaliser to England, according to defender Christophe Berra. It was the first time Kane had captained England at the senior level. "It has been a long season, but there is one more to go before we get a little break". Great credit to him, under pressure he delivers two outstanding technical finishes. "I was trying to get a good contact on it and side-footed into the net", he said. I see body language which says we are still in the game.
The 114th meeting of global football's oldest rivals initially looked to be going the visitors' way after substitute Alex Oxlade-Chamberlain hushed the Hampden roar.
"Obviously I do not know what the gaffer's feeling is on it".
The draw leaves England looking assured of winning the qualifying group, bar any late collapse, but means Scotland still face a tough task to pip Slovakia and Slovenia to the play-off spot.
Kane's late response was cruel for Scotland, whose supporters had been vociferously celebrating a thrilling turnaround, meaning they remain in fourth place on eight points with four matches still to play. "You get hit and they keep coming back and back, creating chances". "If you look at the fixtures we've got, we're capable of winning them all if we can perform like that".
Hart was slated for his contribution to Leigh Griffiths' double free-kick, as well as a moment of madness that involved a back-pass. It looked like we would go on and win the game at that stage, but out of nowhere they score two freekicks. "Harry is one of a number of people I could have given that opportunity to, a few others have done it already and I wanted to give him that boost", he said. I played under Hugo Lloris, France's captain who I will see on Tuesday. We know how good this England side are. I don't think he did much all game.