The United loanee lashed in a free-kick five minutes before half-time after a lay-off from Alex Pritchard when the Black Cats needed it the most.
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It was the forward's 14th goal of the season while he has led the club with fine form to the play-offs this campaign.
And his effort saw the Stadium of Light erupt at a time when they were trailing after Elijah Adebayo scored the opener for Luton.
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Pritchard rolled a free-kick into Amad's path, who has a penchant for the spectacular.
And the 20-year-old had Sunderland fans out of their seats once again with his sumptuous strike, which turned the game on its head.
The Black Cats took complete control of the tie afterward and would have been gutted to hear the half-time whistle.
The domination did not stop there as they went on to take the lead after the break.
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Jack Clarke, once of Tottenham and Leeds, delivered a fine cross for Trai Hume to power a header past Ethan Horvath in the Luton net.
And it proved pivotal as Sunderland went to claim a 2-1 win over the Hatters, with help from their star boy.
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United are keen to see Amad continue his development, they would have been delighted that the youngster can turn up in the biggest of moments.
Both sides are desperate to make it to the Premier League and the atmosphere has been rocking as a result.
Luton have been in stunning form this season after finishing third in the Championship having lost just twice since Christmas.
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While Sunderland scraped into sixth after a jaw-dropping end to the campaign, where they went unbeaten in nine matches to sneak in ahead of Millwall on the final day of the regular season.