Chris Paterson kicked five penalties and Dan Parks dropped a goal to give Scotland their first Calcutta Cup win since the famous 19-13 success in 2000.
Charlie Hodgson replied with four penalties of his own but Andy Robinson's side lacked the cutting edge to capitalise on their superior possession, especially in the first half.
Frank Hadden's revitalised side have now beaten England and France in Edinburgh this season in a remarkable turnaround under the new coach.
It was Scotland who started with the greater purpose, full-back Hugo Southwell and back-rower Simon Taylor running with real intent at the England back line.
And after England prop Andrew Sheridan was penalised for handling in a ruck, Paterson kicked the home side ahead in the third minute.
England hit back five minutes later though, Hodgson slotting his first penalty following concerted pressure from the visiting pack.
In the 23rd minute England's second-rower Danny Grewcock was sin-binned for taking Alastair Kellock out off the ball, but England's pack responded magnificently.
They worked their way up the field but failed to take advantage of their possession and when the Bath lock returned, that fact was magnified when Ben Cohen knocked on with the line at his mercy.
Taylor knocked on from the kick-off in the second half and Scotland were penalised for offside, gifting Hodgson the simplest of penalties to put England 6-3 ahead.
Paterson replied almost immediately to level the scores and England transgressed again in the 48th minute to allow the Edinburgh wing to kick Scotland ahead.
Hadden introduced Nathan Hines for Scott MacLeod on 52 minutes in a bid to stiffen the Scottish pack, and five minutes later Parks struck a beautiful drop goal to increase his side's lead to 12-6.
Hodgson reduced that cushion after Scotland winger Sean Lamont was penalised for a high tackle and Robinson immediately also sent on Lawrence Dallaglio in place of Martin Corry.
Chris Cusiter and Gordon Ross were in the half-back berths for Scotland now and they plotted their way into the England 22 with 10 minutes remaining, Ally Hogg falling just inches short of the opening try.
Nevertheless, Paterson re-opened his side's six-point lead when replacement Simon Shaw was penalised at a ruck with six minutes remaining.
Hodgson struck a minute later to give England hope but Paterson replied with two minutes to go to seal a famous triumph.