Paes and Martina beat Australians Casey Dellacqua and Matt Reid 6-2, 6-3 in a second round match at Melbourne Park in 54 minutes.
The Indo-Swiss pair got an early break in the fourth game of the first set. They led 5-2 shortly after and then broke their opponents' serve again to claim the first set in 24 minutes.
Paes-Martina hit six aces, two more than their opponents. They also hit two more winners, managing 21 in the match.
Hingis played from the baseline while Paes dominated the net proceedings. The experienced pair maintained momentum in the second set, breaking in the eighth game to pull ahead 5-3.
They then held their serve to finish off the match, pocketing 55 of the 96 total points played.
The unseeded Indo-Swiss combination will next face the winner of another second round match between Samantha Stosur-Samuel Groth and Darija Jurak-Jean-Julien Rojer on Tuesday.