"No negatives today, it was about getting through", Martinez said.
Belgium very almost equalised straight away.
The Tottenham star now has the distinction of scoring the longest-ranged header in World Cup history, scoring from 18.6m.
The comeback began just a few minutes later.
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The win also kept South Korea from joining the list of Asian Football Confederation ( AFC ) members without a victory. Mexico next faces the victor of Group E and, Alcocer concedes, "We have to more careful about everything".
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"The Belgian prime minister obviously felt he needed to get in quick from the first whistle", a senior United Kingdom government official said.
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Now, the defensive midfielder says it's time for a new generation to shine: "Hopefully they can achieve something. Four years ago, Messi led Argentina to the World Cup final, but the two-time champions lost to Germany.
The Japanese defence had made a mess of clearing the ball after a punch out by the keeper, who was then off his line when Vertonghen headed back across the goal, the ball drifting in under the bar at the far post.
Jan Vertonghen brought it back to 2-1 with a looping header.
Again, the goal wasn't the prettiest Belgium have scored this tournament, but was a sign of their ability to mix things up when their Plan A isn't working.
At the other end, Courtois saved Keisuke Honda's wickedly curling free shot which led to the winning goal.
The keeper then launched the ball to Kevin De Bruyne, who made a beeline through the field before finding Meunier, whose cross was met by Chadli for the victor.
Both teams fought a tight midfield battle but their forwards froze in the area and Belgium's wide players, Meunier and Yannick Carrasco, did not take risks going forward, effectively turning a 3-4-3 formation into a more conservative 5-2-3 system.