Hernandez converted his only two break chances Monday to end a 12-match losing streak on the ATP World Tour, including all eight this year in straight sets. Mathieu, the 2007 champion, squandered four of his five break opportunities.
The Frenchman received a wild card after coming back from an offseason groin injury that prevented him from starting the season until last month. He lost to Hernandez for first time in four matches.
Starace landed 88 percent of his first serves and converted four of seven break chances to get his first win on the main tour since January.
Starace took a 4-0 lead before dropping serve at 5-2. But the 73rd-ranked Italian immediately broke back to take the opening set.
In the second set, both players held serve until the 12th game, when Luczak could not force a tiebreaker and Starace converted his third match point.
Starace improved to 3-1 against the 75th-ranked Australian.