Barca desperately needed a victory in Ukraine as they battle to progress to the knockout rounds of the Champions League.
After a goalless first-half, it was the Spanish youngster who managed to put the away side ahead.
A cross from Oscar Mingueza found its way to Fati inside the box.
And the 19-year-old made no mistake as he lashed an effort into the roof of the net.
It was a brilliant finish and you can view it below...
Fati then dedicated the goal to his teammate, Sergio Aguero.
The Argentine had to come off in Barca's game against Alaves with breathing problems.
He was later diagnosed with heart arrhythmia and will be out of action for at least three months.
Fati showed he was thinking of Aguero as he did the Argentine's signature celebration.
You love to see it.
Barcelona held on to clinch a vital three points.
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They have leapfrogged Benfica up to second in Group E, having picked up six points from their four games.
Barca can clinch their spot in the last-16 if they beat the Portuguese side at Camp Nou on November 23.
Fail to win and Barca may have to beat Bayern Munich in Germany to progress through the group. What a daunting task that would be.