England's new-look side gave interim coach Stuart Lancaster the best possible start by claiming a first win at Murrayfield in eight years.
Charlie Hodgson's charge-down try at the start of the second half plus eight points from the boot of debutant Owen Farrell left Scotland ruing a series of blown try-scoring chances.
England's inexperienced players came through their baptism of fire with great fight and resolve, despite waves of Scottish pressure.
Dan Parks landed two penalties but dithered with his clearing kick to hand Hodgson and England the softest of tries and the perfect start to their Six Nations campaign.
Scotland seemed certain to score in the last quarter only for Ross Rennie to mis-time the final pass with men outside him, while Greig Laidlaw was ruled not to have touched down as he dived for the ball with the desperately covering Ben Youngs.
It means Scotland have failed to score a try in five of their last six home matches against the auld enemy, with all their pre-tournament optimism blown away by elementary errors at key moments.
It was the predictably frenetic opening, Jim Hamilton barging through weak English arms before being hauled down and England then getting turned over on their first foray into the Scottish 22 after Brad Barritt thumped fellow debutant Lee Jones backwards.
Tidy it was not - both sides knocking the ball forward - and when Parks put a clearing kick straight down Ben Foden's throat, the full-back's scything run led to a penalty from 40 metres that Farrell pushed to the right of the posts.
The errors continued. Hodgson's pass on his own 10-metre line went to ground; Chris Robshaw's simple pass with Chris Ashton in space on the left sailed through the wing's outstretched hands; Scotland attempted a long line-out that fell into no-man's land.
Confusion between Parks and Rory Lamont gave Strettle the chance to dart deep into enemy territory, and this time Farrell landed his first points in international rugby with a simple penalty from 25 metres out.
Parks brought the scores level two minutes later when England went off their feet after Phil Dowson spilled the re-start, and Max Evans then chipped ahead after haring down the left to trigger sustained Scottish pressure.
When Ashton was caught in possession by Chris Cusiter, Parks made it 6-3 with his second penalty from close in.
England's errors were handing Scotland the initiative, sparking the capacity crowd into life on an evening that was fresh but never freezing.
Within seconds of the second half getting under way, the impetus changed dramatically. Parks dithered for an eternity five metres from his own try-line, Hodgson charged his kick down and slid onto the loose ball for the only try of the contest.
Farrell added the conversion for 10-6, and Parks's night went from bad to worse as he missed touch with another kick and then let the ball bounce into touch, to the dismay of the home support.
The impressive David Denton charged down the left wing and when England counter-attacked - Ashton combining with Farrell for an overlap with the Scottish defence stretched - the young back-rower made a brilliant try-saving tackle on David Strettle after Hodgson's cross-kick looked certain to put the winger away for England's second try.
At last the game was alive. Richie Gray smashed through a wrong-footed England rearguard only to lose the ball attempting an ambitious offload, and with England going backwards from their scrum, Scotland's forwards tore into the white shirts only to be penalised for not rolling away.
With 20 minutes to go coach Andy Robinson threw on four replacements and almost triggered an immediate impact.
Ashton chased back to snaffle a kick ahead and save the day, and then Laidlaw sprinted on to another only to be denied when the Television Match Official ruled after countless replays that the fly-half had just failed to touch down.
Then it was Rennie to smash through. This time Scotland seemed certain to score - the open-side had men free outside him and only full-back Foden ahead - but the pass was delayed and the ball went to ground once again.
England were hanging on as the minutes ticked away. Matt Stevens, Lee Dickson and Jordan Turner-Hall were thrown into the line with Farrell moving to fly-half, joined moments later by two more debutants in Ben Morgan and Geoff Parling.
Farrell had a pot from halfway that stuttered two metres short and the tension grew still further.
Scotland then failed to release midway inside their own half, and this time Farrell belied his young years to drill the penalty between the posts for 13-6.
England grew in strength, making their tackles, keeping their discipline, and when the final whistle went their celebrations told their own tale.
Scotland: R Lamont; Jones, De Luca, S Lamont, Evans; Parks, Cusiter, Jacobsen, Ford, Murray, Gray, Hamilton, Strokosch, Rennie, Denton.
Replacements: Laidlaw for Parks (57), Blair for Cusiter (59), Cross for Jacobsen (75), S. Lawson for Ford (75), Kellock for Hamilton (59), Barclay for Strokosch (59).
Not Used: Morrison.
England: Foden; Ashton, Barritt, Farrell, Strettle; Hodgson, Youngs; Corbisiero, Hartley, Cole, Botha, Palmer, Croft, Robshaw, Dowson.
Replacements: Brown for Barritt (72), Turner-Hall for Hodgson (63), Dickson for Youngs (63), Stevens for Corbisiero (63), Parling for Palmer (59), Morgan for Dowson (68).
Not Used: Webber.
Ref: George Clancy (IRFU).