Ilkay Andoan opened the scoring with a goal for City 12 seconds after the start, in the fastest goal in the history of the Federation Cup final.
Marcus Rashford equalized for United from the penalty spot after a handball from Jack Grealish, and the return to the video assistant referee in the 33rd minute.
But 6 minutes after the break, Gundogan restored City’s lead after he met a free kick carried out by Kevin De Bruyne, and hit a direct ball from outside the penalty area, past goalkeeper David De Gea.
City, led by coach Pep Guardiola, won its second title this season, after winning the Premier League last month.
The team dreams of completing the treble and winning the Champions League title for the first time, when it faces Inter Milan in the final a week later.
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