Rusedski, making his debut in the tournament, established his authority with a break in the first game.
Two further breaks helped the 12th seed to secure the first set 6-1.
The second set was a much closer affair and Hipfl had chances to break in Rusedski's first service game.
But the Austrian could not convert them and after that he won just three points against the booming serve of the Briton.
The set went to a tiebreak where Rusedski came up with some more big serves to take it 7-2 and move through into the second round.
But he will not be joined there by compatriot Jamie Delgado, who lost in straight sets to 15th seed Fernando Vicente.
The Spaniard beat the 24-year-old from Birmingham 6-4 7-6.
Thirteenth seed Alberto Martin was upset by Ramon Delgado in three sets, 6-4 4-6 7-5.
Martin's fellow Spaniard Galo Blanco, seeded 14, was another early casualty, losing to Michael Joyce, again in three sets.