The joint ATP-WTA tournament is being played for the first time at the new Queensland Tennis Centre.
In other men's matches, American Taylor Dent beat Steve Darcis of Belgium 7-6 (0), 6-2 and will play Gasquet in the second round.
Two other Americans failed to advance. Fourth-seeded Robin Soderling of Sweden beat Sam Querrey 6-3, 6-3 and Julien Benneteau of France downed Robby Ginepri 3-6, 6-3, 7-5 to advance to a second-round match against Soderling.
Among first-round women's matches, second-seeded Victoria Azarenka of Belarus defeated Ukrainian Kateryna Bondarenko 6-0, 6-2 and third-seeded Marion Bartoli of France beat Australian Monika Wejnert 6-1, 6-2. Jarmila Gajdosova of Slovakia beat China's Peng Shuai 6-4, 6-2.
Seventh-seeded Maria Kirilenko of Russia withdrew Sunday due to an unspecified illness. She was scheduled to play Samantha Stosur of Australia in the first official center court match at the 5,500-seat Pat Rafter Arena.
Hometown favorite Stosur will now play Japanese veteran Ai Sugiyama in the first round.
Top-seeded Ana Ivanovic plays her first-round match Monday night against Petra Kvitova of the Czech Republic while men's top seed and Ivanovic's Serb compatriot Novak Djokovic, the defending Australian Open champion, plays his first match Tuesday against Ernests Gulbis of Latvia.
Djokovic, 21, said Sunday he spent 10 days in the Serbian mountains and two weeks preparing on court in Monaco to get ready for his Melbourne title defense.
"I take the best memories of my career out of Melbourne last year, and I really look forward getting back there,'' he said.
"Of course there's going to be a certain amount of expectations and pressure as the Grand Slam champion but I will try to use it in my favor and look at it as a positive challenge.''
Djokovic could move ahead of Roger Federer and into the No. 2 spot in the rankings, behind Rafael Nadal, if he wins in Brisbane. His biggest threat comes from second-seeded Jo-Wilfried Tsonga of France, the man he beat in the Australian Open final last year.
Djokovic is just 10 points behind Federer, who is starting his year playing an ATP event in Qatar. Neither are defending any points so Djokovic can move ahead of Federer if he wins the inaugural Brisbane event.
His first-round opponent Gulbis is well-known to him - they both trained as teenagers at the same German tennis academy. Gulbis pushed Djokovic hard in two matches in 2008.
"He has nothing to lose,'' Djokovic said. "He's a big server and for both of us the first match of the season, so it's tricky.''
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