The Seagulls had already taken the lead through Joao Pedro in the first-half before the summer's second big signing also got on the scoresheet.
Fati, on loan from Barcelona, finished off a brilliant move just before the hour mark to put Brighton 2-0 up against Ajax at the Amex Stadium.
It came from some brilliant play from Simon Adringra, whose lovely little dink found the Spain international.
Fati executed a delightful first touch to control the ball before finishing with his second, all in one movement, in a slick piece of skill.
And the 20-year-old was inches away from doubling his own personal tally just moments after kick-off, flashing a shot just past the post.
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The forward had been tipped for stardom at Barcelona after breaking into the first-team at the age of 16.
Injuries have stunted his development somewhat but he looks like he is back on the right path, fitting in well with Brighton's fluid attack.
The second goal gave Brighton the confidence to see out the match, their first victory in Europe after a loss and a draw so far this campaign.
And what a team to win against, a side that have four Champions League titles in their trophy cabinet throughout their history.
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However, Ajax are a shadow of their former selves as they continue as they look for their first win in the Europa League this season.
They are already in crisis-mode, sitting in the relegation zone in the Eredivisie with one win in seven matches.
Pedro had put Brighton a goal up just before half-time after following in Kaoru Mitoma's shot to bundle in the rebound.
And while Ajax started the second-half the better side, the home doubled their lead to wrestle control of the tie.
Fati's goal was exactly what Roberto De Zerbi needed to give them a first win in six matches.
It had been a miserable October without a win all month before Thursday night.
And despite violence breaking out before the match between fans and police, it was a good night for Brighton after a disappointing few weeks.
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