Josh Brookes (Suzuki) was the first Australian home in race two in 15th position.
In race one, the 40-year-old Biaggi scored a comfortable victory over fellow Italian Marco Melandri.
Bryan Staring was the leading Australian, making up eight spots from qualifying to finish 10th on his privateer Kawasaki.
While Biaggi enjoyed clear air out in front, there were a number of battles behind him, including a fierce arm wrestle for second place between the BMW of Melandri and Frenchman Sylvain Guintoli on a Ducati, who came in third.
After the first of 14 rounds, Biaggi leads the title race on 45 points ahead of Melandri (30), British rider Sykes (29) and Checa (25).
- AAP