Fifth-seed Bautista Agut, who won the title in 2016, outlasted second-seed del Potro, the 2009 champion, in a match of remarkable highs and lows.
He targeted the Argentinian's backhand with confidence and when he switched to the forehand court del Potro's return placement was off in the first set.
Unlike del Potro who had a tough semi-final against Spain's David Ferrer, fellow Spaniard Bautista Agut had an easier run through the tournament on the same side of the draw where first and third seeds Jack Sock and Sam Querrey lost in the early rounds.
It was a different del Potro in the second set as he started to find his range and eventually broke Bautista Agut at 5-4 to take the set and level the match.More news: Power expected to be restored to Puerto Rico by March
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"I gave everything I have on the court this week", said the world number 21 after the match.
Earlier, fifth seed Bautista Agut outlasted Dutchman Robin Haase in an epic clash that took nearly three hours before the Spaniard produced an audacious backhand lob that kissed the baseline to clinch the 6-7 (7) 7-6 (3) 7-6 (5) win.
"I served really well in the second set and I tried to play aggressively with my forehand, and I think I did it".
"Today the conditions were hard and he was a hard opponent, serving very well and a lefty, playing with a very flat backhand", Bautista Agut said. I knew it was going to be important, the beginning of the match. Juan Martin was there to fight until the final point, creating a break point that could set up the deciding tie break, but he was denied by an ace from Roberto, one of his most important shots of the day.