Unseeded Russian Mikhail Youzhny denied top seed and defending champion David Ferrer a fourth Valencia Open title when he beat the world number three 6-3, 7-5 in the final of the Spaniard's home event on Sunday.
Top seed Roger Federer suffered a shock 6-3, 6-4 defeat to Germany's Daniel Brands in his opening match at his home Swiss Open on Thursday - the latest setback for the former world number one.
World number 30 Berrettini saved five points in the marathon second set tiebreak and held on to win it 13-11 for his third ATP crown in last 11 months.
Italy's Matteo Berrettini overcame second seed Roberto Bautista Agut 7-6(9), 6-4 to win his first title at the Swiss Open in Gstaad on Sunday.
De Minaur, 20, went the entire tournament without facing a break point, and the Australian fittingly clinched victory with a deft serve-and-volley backhand winner.
Roger Federer got his delayed hardcourt season off to a positive start with straightforward 6-3, 7-6 (7) win over Germany's Phillip Kohlschreiber to ease into the third round of the Western and Southern Open on Tuesday.