Iheanacho opened the scoring midway through the first half when he prodded in after playing a one-two with James Maddison.
The two combined again before the break to almost score a second but this time Braga goalkeeper Matheus made a superb diving save to deny Maddison.
But Iheanacho got his and Leicester’s second soon after the restart when his shot from the edge of the area took a heavy deflection to land in the back of the net.
That prompted a dominant spell for the hosts, with Iheanacho going close to completing his hat-trick, but his shot was kept out by Matheus.
A third for Leicester duly arrived with Iheanacho this time turning provider, squaring a pass for substitute Dennis Praet to tap in, and Maddison wrapped up a brilliant win when he forced his way through the defence before finishing.
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