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.
Southgate refused to blame his side for conceding the second late free-kick from which Scotland scored, and is happy group leaders England still have qualification for Russian Federation in their own hands - although Slovakia will close with two points by beating Lithuania, while Slovenia are three points back.
However, Kane slammed in at the far post deep into stoppage time to break the hearts of the Tartan Army.
The remarkable finish leaves England still comfortably in charge of the group but Scotland still with a lot of work to do if they want to spend next summer in Russian Federation.
"It is a special day", said Tottenham Hotspur striker Kane, whose side had taken the lead through Alex Oxlade-Chamberlain goal in the 70th minute.
"We had a couple of the marines come to the game and watch us, so it was great to see them again".
"The atmosphere in the changing-room would have been a party if we'd won", he said. The substitute curled an incredible pass between Scotland's back three and Kane drifted in to stab home in the third of four added on minutes.
HARRY KANE admitted his last-gasp England goal saved his captaincy celebration from going sour.
England's first chance arrived after 17 minutes when Harry Kane blazed the ball over the bar. "The objective is to qualify and we're top of the group".
"I have got to say it was like watching a heavyweight boxer versus a middleweight".
"We can only take steps at a time and work as a team to improve every area - whether that's technical, tactical, psychological". We have a great point against a very good England side who, no doubt, will be going to the World Cup. Griffiths' profile south of the border, where he had an underwhelming spell at Wolves earlier in his career, is certainly much higher now and Kane chose to accentuate the positives of his contribution rather than examine England goalkeeper Joe Hart's failure to keep them out. You can get moments in football, like today, where someone produces unbelievable quality and you find yourself level or behind in a game with the momentum against you and all of the crowd on a huge high.
"I've a feeling we might have been sitting here talking about how long it was since he last scored for England if he hadn't scored".
"The end for me is a significant moment because the character of the team has to come through in these moments", said England manager Gareth Southgate, whose side face France in a friendly in Paris on Tuesday.
"I felt we controlled the game for large parts and opened the scoring". I don't think it was tougher than what we expected because we always expect to have tough games, especially against your rivals. "All sorts of emotions", Strachan told reporters.