Jones had 11 aces and didn't drop serve in a 7-6 (9-7), 6-2 decision over Melzer. He won 82 percent of the points on serve, losing 10 points in 10 games.
Santiago Giraldo raced into the second round with a 6-1, 6-0 romp past Go Soeda in 40 minutes. Giraldo finished off five of his eight break chances, taking more than 60 percent of the points when receiving serve.
He dropped eight points in seven games serving, winning 69 percent of the points in the match.
Lu Yen-Hsun defeated Benoit Paire 6-3, 2-6, 6-2 and earned a spot in the second round opposite top-seeded David Ferrer. One of his three breaks came in the third set but he countered that with three of his five total breaks of Paire's serve.
Igor Sijsling was among three qualifiers winning first-round matches Tuesday, defeating Robin Haase 3-6, 6-3, 7-5. Also, Jesse Levine stopped Daniel King-Turner 6-2, 6-2, joining Jones and Sijsling as qualifiers in the second round.
Other first-round results Tuesday saw Lukas Lacko beat Paolo Lorenzi 6-3, 6-3; Gael Monfils get by Benjamin Becker 6-7 (2-7), 6-3, 6-4; and Alejandro advance when Grega Zemlja, down 6-4, 3-1, retired.
Swim Week Miami Beach 2014 [PHOTOS]