The Austrian world No. 28, who had a personal best 36-29 record in singles during 2009, served strongly and converted two of eight break points to beat Fognini.
Melzer, who was the only seeded player in action Monday, will play either Germany's Florian Mayer or French wild card Sebastian Grosjean in Wednesday's second round.
Story continues below ↓advertisement | your ad hereThe tournament's top four seeds - Spaniards Tommy Robredo, David Ferrer, Juan Carlos Ferrero and Nicolas Almagro - all received byes into the second round.
Unseeded Brazilian Thomaz Bellucci, ranked 34, beat Switzerland's Marco Chiudinelli 6-3, 6-3 in only 64 minutes.
The left-hander won his first ATP singles title at Gstaad in 2009 and became the first Brazilian since Gustavo Kuerten in 2004 to break into the world's top 50. He maintained a high first-serve percentage throughout Monday's match and converted three of four break points in an impressive win.
"I'm very happy. I played very well today and feel confident for the next round," Bellucci said.
"For sure, my serving was helping me today and that was always a big point for me."
Bellucci will play either former champion Philipp Kohschreiber or qualifier Inigo Cervantes-Huegin of Spain in the second round.
New Zealand wild card Rubin Statham beat his compatriot and Davis Cup teammate Dan King-Turner 6-2, 7-5 in Monday's only other first-round match.
© 2010 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.Primera Liga round-upClijsters wins opening match at Brisbane
