The sides were level at 9-9 at halftime but England scored 10 points - through Toby Flood's fourth penalty and a converted try by replacement flanker Tom Croft - while the Scots were down to 14 men following John Barclay's sin-binning to go 19-9 up with 13 minutes left.
Scotland winger Max Evans' well-taken try in the 74th set up a tense finale but England added three points through Jonny Wilkinson's penalty and held on for a fourth straight win, despite failing to impress in a scrappy Calcutta Cup match - the oldest fixture in rugby union.
"It was one of the most difficult games I have ever played at Twickenham," said England flanker James Haskell, whose tireless work rate and lung-busting running earned him the man-of-the-match award. "Scotland made it so difficult for us."
If Martin Johnson's side beat Ireland in Dublin next Saturday, the team will clinch the Grand Slam of five straight victories in the northern-hemisphere competition - also its first in eight years. Only second-place Wales, which is away at France on Saturday, can stop England landing the title, although a points difference of 42 will need to be bridged for the Red Dragons to nick the title.
It was the second ugly win in succession for England, after an equally attritional victory over reigning champion France on February 26.
"All our guys are really flat in there," Johnson said. "But that's not a bad place to be after winning four in a row. All the other teams would love to be in our position. And we have earned it - nothing has come easy.
"But we know we can play better than that."
The try by Croft, on just a minute before barging through Dan Parks' tackle, was one of the few times the English broke Scotland's defensive line and they will probably have to improve massively if they are to down Ireland next weekend.
"Winning the game was the most important thing," said England captain Mike Tindall, who lasted just 40 minutes before being withdrawn with a left ankle injury. "We're not happy with how we played but all credit to Scotland - they took the game to us and we also made it hard for ourselves."
Scotland, which hasn't won at Twickenham since 1983, remains without a point in the competition and heads to Italy for its last match needing a win to avoid the wooden spoon for the last-place finisher.
Fullback Chris Paterson kicked eight points for Andy Robinson's side, while flyhalf Ruaridh Jackson added a drop goal for the visitors.
Flood and Paterson traded two penalties each in an imprecise opening 26 minutes before England started to see more of the ball, without really threatening Scotland's obdurate defense.
The home side was also bossing at scrum time, and a third penalty awarded against the Scots in that department allowed Flood to knock over a simple kick for 9-6 in the 30th.
A rare foray upfield by Scotland resulted in Jackson dropping a goal from long distance to take the teams into the break level at 9-9.
England's back line continued to be ponderous, however, although an inspired break by Chris Ashton - a scorer of six tries this tournament - enlivened the subdued crowd in the 42nd. When the ball was recycled, Flood helped send Tom Wood in down the left but the flanker was stopped just short of the line.
Barclay was sin-binned in the 57th for killing the ball as England closed in on Scotland's line, allowing Flood the simplest of tasks with a penalty in front of the posts and handing the initiative back to the hosts.
"It was disappointing to lose John at that stage," said Robinson, who was critical of a number of other decisions made by the officials.
At 12-9 ahead, England looked to grab the score that would take the team beyond the reach of Scotland but a superb last-gasp tackle by Paterson denied Foden a try in the left corner in the 65th.
But just as Barclay was about come back on, Wilkinson spread play from right to left, Cueto sent in Croft and the rangy flanker thundered through an attempted tackle by Parks to ground in the corner.
Wilkinson converted but Evans gave Scotland hope by chipping over England's flat defense and gathering to scurry over for a try converted by the flawless Paterson.
With nerves frayed, the ice-cold Wilkinson stepped up in the 79th to slot over a penalty to take the match beyond the visitors.
