Three first half tries, including a double from Huw Jones, laid the foundations for a famous Scottish victory, its first over England since 2008, to end the Grand Slam hopes of the visitor.
England had won 24 of 25 internationals going into the match as heavy favorite, but Scotland never trailed after an early penalty from Greig Laidlaw and went on to dominate the opening half.
Jones took advantage of sloppy English defence to dart over for his opening try, the first scored by Scotland at Murrayfield against its arch-rival since wing Simon Danielli went over 14 years ago.
Owen Farrell, who the BBC reported at halftime was involved in an unseemly pre-match scuffle with Ryan Wilson, responded with his second penalty before Sean Maitland went over in the corner after a superb pass by man of the match Finn Russell set up the try.
The icing on the cake was to follow as Jones demonstrated his electric pace to burst through the English defence, shrugging off several tackles to go over near the posts, his eighth try in eight Tests.
Laidlaw's conversion gave Scotland a 22-6 halftime lead and left England with too much to so.
Farrell scored an early converted try to raise home jitters which increased to fever pitch as he crossed again only for his effort to be ruled out for a knock-on as Courtney Laws tackled Scotland captain John Barclay.
It was the slice of good fortune that the host needed and after England replacement Simon Underhill was yellow carded it was left to Russell to apply the final touches with a penalty to leave his side 12 points clear.
England coach Eddie Jones was not making excuses for his team's disappointing defeat.
"Congratulations to Scotland they were too good for us," he said.
"Full marks to them. We did not meet the challenge today."
Stockdale double lifts Ireland
Earlier, Ireland kept its Grand Slam hopes alive by holding off a spirited Welsh fightback in Dublin for a bonus point 37-27 win.
Wales, trailing 30-27 with a minute to go, was pushing for a late score but Jacob Stockdale intercepted a floated pass to run in his second try of the match and seal the Irish victory.
Stockdale, whose early try put Ireland ahead in the Aviva Stadium, was scoring his eighth in the last seven Tests.
A first half try from Gareth Davies and eight points from the boot of Leigh Halfpenny saw the visitor cancel out Stockdale's early effort to lead 13-5.
But Johnny Sexton landed a penalty and New Zealand-born Bundee Aki barged over for a try, converted by Sexton, to give the home side a 15-13 advantage at the break.
Dan Leavy and Cian Healy capitalized on that home momentum with second half tries to leave Ireland 27-13 ahead before Wales hit back with tries from Aaron Shingler and Steff Evans.
Conor Murray's late penalty goal and the late, late try from Stockdale ultimately gave Ireland its 10th straight win and one hand on the Six Nations trophy.
However, resurgent Scotland visit Dublin next before what had been billed as a Grand Slam and title decider against England at Twickenham on St Patrick's Day, March 17.
France ends winless run
Friday night saw France end its eight-game winless run with a 34-17 victory over Italy in Marseille.
Toulon centre Mathieu Bastareaud starred on his return to the side after a suspension for a homophobic slur, scoring one of the three French tries, with Paul Gabrillagues and Hugo Bonneval getting the others.
France also coped without a number of regular starters, dropped by coach Jacques Brunel for "inappropriate behaviour" after the narrow defeat to Scotland in the second round of matches.
Italy led early in the first half after a 10th-minute penalty try canceled out Gabrillagues' unconverted score, but France was ahead by the half as Maxime Machenaud kicked two penalties to make it 11-7.
Second half tries from Bastareaud and Bonneval put the game out of Italy's reach in the second half, with Machenaud kicking his way to a personal points tally of 17.
Matteo Minozzi got a consolation try for Conor O'Shea's men, but it was too little too late for Italy.