But Jonny Wilkinson, who otherwise endured a torrid night with the boot, dropped a goal and landed a penalty to bring England back within touching distance.
Chris Ashton then scored the match-winning try three minutes from time - his sixth touchdown of the tournament - to seal England's passage.
And that left Scotland praying for a miracle. Andy Robinson's men will be on the plane home if Argentina pick up even a losing bonus point against Georgia on Sunday.
"We let them get the initiative. Things weren't quite going our way. Scotland had a bit more urgency but we got ourselves back into it," Johnson said.
"To come back from 12-3 down and win was good.
"They had the initiative in the first half but we felt if we held onto the ball we would create opportunities.
"The way the guys handled half-time was really good. To come back and win the rest of the game 13-0 was good. There is a lot to get better at now we go to the quarter-finals.
"We are making it very hard for ourselves at times but we showed character to get ourselves out of a pretty tough hole.
"Whoever scored the first try today was going to get over the line and we held our nerve.
"Chris put the try away well at the end and we showed a lot of character to win the game.
"The guys who came on did pretty well and the subs all had a good impact and we got on top of them.
"The game is not always going to be beautiful. There was some chaos out there, feet flying around and all that stuff that you need to deal with. It has been a very gritty group."
Wilkinson will be sent for a scan on the forearm injury, which forced him off with five minutes remaining. The Toulon fly-half appeared to be in instant pain when he suffered the blow in a tackle.
England will also be sweating over a potential citing for wing Delon Armitage, who caught Chris Paterson with a high tackle.
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