Adnan Januzaj's 51st minute strike proved to be the difference between the teams who were playing their third and final Group G game.
With this win, Belgium took their points tally to nine, while England have six points as they finished top-two in this group to enter the second round.
In the next round, Belgium will meet Japan, while England will take on Colombia.
In Saransk, Tunisia defeated Panama 2-1 in the other game of the group to finish third with three points from three games. Tunisia and debutants Panama are eliminated from the tournament.
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