England now move on to a last-four date with either Russia or Croatia, who meet in the remaining quarter-final clash later on Saturday.
The opening stages of the game passed by without incident as both teams appeared slightly overawed by the possibility of progressing further in the competition and it took a 30-yard strike from Sweden's Viktor Claesson to break the tension.
England were struggling to get into their stride and it took until the 19th minute for their first opportunity to arrive with Harry Kane dragging wide from 20 yards after good work from Raheem Sterling.
By the end of the opening quarter, England were beginning to show more ambition and the Three Lions opened the scoring from another set piece with Maguire powering a header into the bottom corner from 12 yards after meeting Ashley Young's corner.
England continued to set the tempo with the ball regularly being worked down either flank and an opportunity to double their advantage arrived just before the break.
Sterling expertly controlled a long ball before seeing his attempt to round Robin Olsen halted, but the winger then failed to be decisive when getting a second opportunity and instead of passing to Kane who was waiting 16 yards out, a shot was deflected wide.
Sweden needed a change in approach, and immediately after the restart they almost found an equaliser when a cross was delivered for Marcus Berg at the back post, but the forward's header was superbly kept out by the left hand of Pickford.
However, while Sweden were pressing forward, the space was opening up for England at the other end and just before the hour mark the lead was doubled when Alli was picked out by Jesse Lingard and the Tottenham Hotspur midfielder sent a header into the roof of the net from eight yards.
England were in control but Sweden almost produced an immediate response within two minutes as a terrific move ended with Claesson firing towards the bottom corner from the penalty spot, only for Pickford to save to his right before Jordan Henderson blocked the rebound.
Maguire could have scored his second of the game but volleyed over at the back post and although England headed into the final quarter without conceding, Sweden remained a constant threat.
Again, it was Berg who was proving to be the biggest danger but after the forward had turned inside the box before getting a volley away, Pickford tipped his effort over the crossbar.
That opening reminded England that the game was far from over but it resulted in no complacency during the closing 15 minutes as Sweden failed to creating anything of note in the final third.
Southgate had the luxury of replacing the likes of Henderson and Sterling, and England will now turn their attention to Wednesday night where they will have the opportunity to reach their second World Cup final.
SWEDEN (4-4-2): Olsen; Krafth (Jansson 85'), Lindelof, Granqvist, Augustinsson; Claesson, Ekdal, Larsson, Forsberg (Olsson 65'); Toivonen (Guidetti 65'), Berg
ENGLAND (3-4-2-1): Pickford; Walker, Stones, Maguire; Trippier, Henderson (Dier 85'), Alli (Delph 77'), Young; Lingard, Sterling (Rashford 91'); Kane