Celtic striker Leigh Griffiths took the 87th-minute free-kick and brilliantly bent it inside England 'keeper Joe Hart's left-hand post.
A draw leaves England top of Group F, with Slovenia three points back and Slovakia able to cut the gap to two with victory over Lithuania.
"It was probably one of the most emotional games ever in my managerial career".
England were facing the end of a 34-game unbeaten run in worldwide qualifiers and a first defeat at Hampden Park since 1985 when Kane, Southgate's captain for the day, salvaged a draw in stoppage time.
"To put the work that he put in and then have a free-kick, when you're exhausted at the end of the game, and be able to execute it is phenomenal. That was beyond the call of duty at times".
"I think it's a huge moment for the team", said Southgate, who took his squad to a military training camp on a team-building exercise last week. The questions around us centre on character, centre on the ability to withstand things that go against you and that is what we have to show. We stuck with it and showed tremendous character to come back. Today we didn't stop and a real quality finish got us the point.
There was some trepidation about the visit of England fans and, in the wake of recent events in Manchester and London, security was tightened.
The three goals took his tally during the qualifying campaign to 11, level with Cristiano Ronaldo, who scored twice for Portugal a day earlier.
Naughty Bayern Munich nab Arsenal star on the cheap!
Bayern chairman Karl-Heinz Rummenigge, meanwhile, was pleased to welcome another Germany global to the Allianz Arena. Gnabry netted 11 goals for Bremen in the Bundesliga last season and also finished top scorer at the Olympic Games.
England captain Harry Kane was proud of his side's reaction to Scotland's quickfire double in Saturday's 2-2 draw at Hampden Park.
Strachan had peculiarly called the game a "must perform" encounter but he knew at least a point was required to keep qualification hopes alive.
However, Hampden Park erupted in the 87th minute when Leigh Griffiths curled home a 25-yard free-kick for his first worldwide goal, before lightning struck twice in the final minute of normal time as another set-piece from the Celtic star put Scotland on the brink of a famous Group F victory.
Scotland are unbeaten in their last six home games. Vocal Scotland supporters prepared to savour what would have been their 42nd victory in 114 meetings with England, but were silenced in the dying embers when the prolific Kane cushioned home a volley from close range not long after Gordon had beaten away a powerful Dier free-kick.
"We wanted to come here and win".
SCOTLAND: Gordon 6 - Berra 6, Mulgrew 6.5, Robertson 6.5, Tierney 7 - Brown 6, Armstrong 6.5 - Anya 6 (Martin 6), Snodgrass 6 (Fraser 6) - Griffiths 8.
The hosts welcomed England keen to exact a revenge for the 3-0 defeat in the reverse fixture at Wembley back in November when Daniel Sturridge, Adam Lallana, and Gary Cahill all got on the scoresheet for a comfortable win.
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