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The Argentinian put in a powerful performance to ease past the American fifth seed, winning 6-3 6-2 in Portugal in just 74 minutes.
It was a fast start from Tiafoe, breaking Baez in the opening game, before the 21-year-old secured back-to-back breaks of his own in the fourth and sixth games to edge ahead, ultimately taking the first set.
The second set started evenly, but from 2-2, Baez put his foot down, again breaking consecutive Tiafoe service games, before serving out for the title.
The first serve was the difference for Baez, making 64 per cent of his compared to Tiafoe, who managed just 39 per cent.
Baez was also more effective when he needed his second serve, winning 61 per cent of points, with his opponent winning only 39 per cent from his own second serve.