It was an ultra-defensive start in Samara, with the first sight at goal coming on 18 minutes when Harry Kane shot wide from close range.
The game soon lit up after Harry Maguire rose to thump a header home from a corner right on the half-hour mark.
A presentable opportunity to double England's tally before the break fell to Raheem Sterling, but he dilly-dallied and spurned the chance after rounding goalkeeper Robin Olsen.
The lead was eventually doubled after the break when Dele Alli headed in at the back post following a superb delivery from the right side by Jesse Lingard.
Sweden attempted to bounce back through Viktor Claesson, but Jordan Pickford stretched out his hand to palm away his shot from the edge of the box.
Marcus Berg then failed to steer home from close range, drawing an acrobatic stop from Pickford as Sweden looked for a way back.
However, the Three Lions were in complete control and comfortably saw out the game, and they will now contest their first semi-final at the World Cup finals in 28 years when they face the winner of the other quarter-final between host nation Russia and Croatia.
Sweden: Olsen, Lindelof, Granqvist, Augustinsson, Krafth, Larsson, Ekdal, Forsberg, Claesson, Berg, Toivonen.
England: Pickford, Maguire, Stones, Walker, Trippier, Young, Henderson, Alli, Lingard, Sterling, Kane.