The visitors’ winger Duhan van der Merwe scored the only try of their first away victory in the tie since a 22-12 success in 1983 and just a fifth Twickenham triumph over England in their history as Scotland dominated in all areas.
Van der Merwe’s score ultimately proved the difference in a behind closed doors match where the hosts paid dearly for their indiscipline, even though both home captain Owen Farrell and opposition fly-half Finn Russell kicked two penalties apiece.
“It’s amazing for us, we believed in each other and to a man deserved it,” Scotland captain Stuart Hogg, whose long-range kicking kept England pinned deep inside their own half in a rainswept second period, told ITV Sport.
“We got excited during the week and we knew we could put in a performance. If we got everything right we stood a chance of winning.
“We stood firm defensively, and that was the winning of the game.”
Meanwhile England coach Eddie Jones praised Scotland by saying: “They played tough, edged in the set piece, won in the air and we just could not get in the game. We were not at the races.
“I take responsibility. I didn’t prepare the team well enough. We just had one of those days. We don’t have many, but we had a bad day today.”
Scotland dominated territory and possession in the first half yet they only led 8-6 at the break before Russell’s second penalty proved the only score after half-time.
England, with British and Irish Lions coach Warren Gatland looking on from the otherwise largely empty stands, almost had an early score when lock Maro Itoje charged down Scotland scrum-half Ali Price’s clearance kick.
But England then infringed at the ensuing ruck.
The hosts found themselves repeatedly getting on the wrong side of Irish referee Andrew Brace, conceding four penalties in the opening five minutes.
When they were penalised in front of their posts, Russell - the inspiration behind a comeback from 31-9 down in a 38-38 draw at Twickenham two years ago - kicked Scotland into a 3-0 lead.
Their pressure saw England reduced to 14 men in the 24th minute when No. 8 Billy Vunipola was sin-binned for a high tackle on Russell.
Four minutes later, Scotland almost had a try when Russell’s cross-kick bounced just too high for van der Merwe as the left winger looked to touch down.
But in the 30th minute the visitors’ dominance was rewarded.
After an England scrum, missing injured prop Mako Vunipola and fellow front row Joe Marler, who dropped out of the squad for family reasons, had repeatedly come under strain near their own line, Russell’s cross kick was knocked back by winger Sean Maitland.
The ball was worked across field, with Redpath and Hogg involved before Turner found van der Merwe.
Russell was off-target with the conversion, but Scotland still led 8-0.
Farrell reduced the deficit with a long range penalty and just before half time it was Scotland, with Vunipola back on the field, who were a man down when a replay check saw Russell yellow-carded for tripping England scrum-half Ben Youngs.
Farrell kicked the ensuing penalty and Scotland led by just two points at the break.
But Hogg’s penalty kick for an attacking line-out near England’s line gave Scotland good field position.
Following several drives, England prop Ellis Genge was penalised and Russell, having completed his 10-minute suspension, kicked Scotland into an 11-6 lead.
Full-back Hogg’s kicking out of hand, however, kept England pinned in their own half in testing weather conditions.
With eight minutes left, Hogg missed a penalty from just inside England’s half but Scotland were not to be denied a famous victory.
Elsewhere in Rome, Italy lost 10-50 to France. Wales host Ireland later today (10pm Phuket time).