England substitute Alex Oxlade-Chamberlain opened the scoring just a few minutes after coming on for Gareth Southgate's side, but the Three Lions were stunned by two late free kick from Griffiths, who struck twice from nearly identical positions to put Scotland in front, only for Tottenham striker Harry Kane to score in injury time to deny the hosts a famous victory.
England trained with the Royal Marines in the build up to the match, and Kane praised the determination of the squad.
"The questions around us centre on character and the ability to withstand events that go against you".
Gareth Southgate's Three Lions side had two half-chances in the first half, but they were spurned when Harry Kane miscued a first-time strike after good work from Adam Lallana before failing to capitalise on mistake from Craig Gordon.
As the game neared to an end Leigh Griffiths scored his first goal for Scotland with an incredible free-kick from outside the box which rocketed into the corner of the net.
"I was looking to do the exact same with the second free-kick".
"I should be absolutely delighted with two goals and man of the match, walking in here with three points". Even as I was doing well with my club he was giving me a phone call or text to say, "Things could change for you as you play more and get bigger".
If we had kept the ball better going towards their goal we might have nicked the three points, but you can't switch off against this England side with guys like Harry Kane up top.
England were left in no doubt as to what kind of afternoon awaited them before kick-off when "God Save the Queen", the English national anthem, was drowned out by a volley of Scottish boos.
"We look at opposition set plays before every game and we knew Griffiths had a great free-kick on him", added Kane. We had a couple of marines come here from the weekend to watch.
"The way the game panned out, it was a good point for us".
"When we went 2-1 down a few lads could have been on their knees".
Kane, who was handed the captain's armband for the first time, said: "I would say that is probably the most special moment for me".
In describing the moment Southgate revealed he would captain the team, Kane added: 'It was quite emotional.
Germany's five point lead atop Group C was maintained as Stuart Dallas scored two minutes into injury time to give Northern Ireland a 1-0 win over Azerbaijan in Baku.
"We just tried to take as much as we could from what they told us into our game and I think we stood up and were counted". I don't think it was tougher than what we expected because we always expect to have tough games, especially against your rivals.
England looked more risky on the rare occasions they got their opponents turning and Kane had another half chance, with Craig Gordon stranded after coming out of box to head away a long ball. Tom Heaton has had an outstanding season and we've got to make sure people feel involved.
"I thought he was extremely composed with the ball at his feet and his focus through the week, he's been one of the outstanding leaders in the group", said Southgate, whose side remain top of UEFA qualifying Group F.
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