Penalties from Chris Paterson and Dan Parks gave the Scots an early six-point lead before Jonny Wilkinson sent over his fourth kick after three misses.
A drop-goal on half-time from Parks re-established Scotland's six-point advantage at the break.
Paterson then increased Scotland's lead before an instant drop-goal from Wilkinson again reduced the deficit.
The England fly-half halved the lead with another penalty before Chris Ashton's late try secured victory for the English.
Toby Flood flung the ball wide to the Northampton winger, who powered over in the corner.
England qualify as pool winners while Scotland are likely to miss out on the quarter-finals as Argentina are still to play Georgia.