England looked to be seeing the game out comfortably before Griffiths struck with just five minutes to go - curling a set piece into the right-hand corner of Joe Hart's goal for his first strike in internationals.
Substitute Alex Oxlade-Chamberlain had looked to have put the visitors on course for victory with a 70th minute solo strike, but the sensational finale means Gareth Southgate's men will be delighted to have come away with a point.
Captain Harry Kane led the rescue act as England nicked a stoppage-time equaliser to deny Scotland a famous win on Saturday night.
Griffiths said: "It was a tough ask to get back into the game from 1-0 down but we showed what we are about, great resilience but you can't switch off". It has been a while since I've scored for England and it was special.
The draw keeps England top of their group ahead of Slovenia by three points with Scotland back in fourth.
We were in control at 1-0 up and then all of a sudden 2-1 down and it looks as if you are going away losers.
The turnaround sent shockwaves throughout England's fanbase as they faced their first World Cup qualification group defeat.
"I felt we controlled the game for large parts and opened the scoring".
"It was an important moment for the team and an important moment individually for Harry", Southgate told his post-match media conference.
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"But they stuck their chests out, walked back to the centre circle and said "Let's get something from it".
Seemingly relishing the opportunity, Kane got on the score sheet as he netted a late equaliser following a hectic spell which had seen Scotland come from behind to lead through two Leigh Griffiths free-kicks.
Strachan added: "I saw Scotland's best ever free kick and then I see Scotland's second-best free kick, and then I have a noise that I have never heard anything like before". We had moments where we got into really good positions in the final third and you have got to take the finish. It could be a big point for us.
But in the 93rd minute, the captain, leader and (future) legend Harry Kane latched onto the end of Raheem Sterling's diagonal ball to volley home past Craig Gordon.
"Personally, I picked up a lot about leadership from the time we spent with the Marines".
"You try to protect yourself from the excitement but when we equalised I didn't, because that could have been my best result as a manger".
"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.
"Not only did we discuss how we wanted to play but we discussed how we needed to be if events turned against us".
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