Lorenzi served for the match at 6-5 in the third set and had a 3-1 lead in the tiebreaker, but didn't win a point after that.
The 42nd-ranked Dolgopolov served for the match at 5-4 in the second, but Lorenzi broke back before taking the tiebreaker.
Story continues below ↓advertisement | your ad hereDolgopolov will next meet Croatian wild card Franco Skugor, who routed two-time Umag finalist Filippo Volandri of Italy 6-2, 6-1 in 56 minutes.
It was only the third career ATP-level singles victory for the 22-years-old Skugor, who reached the quarterfinals at the Swedish Open two weeks ago.
Eighth-seeded Juan Ignacio Chela of Argentine also advanced after breaking Ruben Ramirez Hidalgo of Spain four times in a 6-4, 6-1 win.
Top-seeded Nikolay Davydenko and second-seeded Jurgen Melzer, the French Open semifinalist, have a bye in the first round.
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Federer gets tested again at WimbledonGuardiola fined for ref rant
