Centre back Maguire connected with an Ashley Young corner to score his first international goal after 30 minutes as England had much the best of the first half.
Jordan Pickford made excellent saves to deny Marcus Berg, twice, and Viktor Claesson after the break but England generally looked the more dangerous side and were rewarded when Alli headed the second from a Jesse Lingard cross in the 59th minute.
Belgium shun Brazil to reach World Cup semi-finals
England previously reached the semi-finals in 1966, when they went on to win the World Cup for the only time, and 1990 and will next face either Russia or Croatia, who meet later on Saturday
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