The highly-anticipated contest between the world number one and the two-time Roland Garros champion ended after two high-octane sets.
Murray weathered a gallant fightback from Matteo Berrettini before dumping the 13th-seeded Italian out of the Australian Open first round on Tuesday.
The Williams sisters have a remarkable record of winning all 14 grand slam doubles finals they had contested.
Rafa Nadal on Thursday continued his pursuit of a third successive Grand Slam title with a four-set win over Ricardas Berankis.
The 40-year-old will be missing in action based on the advice of her doctors.
