Sharapova cruised her way through the first two rounds winning 6-0, 6-0 against both Russia's Olga Puchkova and Japan's Misaki Doi, and had little more trouble with seven-time Grand Slam winner Williams winning comfortably in straight-sets.
Sharapova broke Williams immediately to start the game twice to race out to a 4-0 lead to give her 28 straight games that she had won to start her Australian Open campaign.
Even though Williams did get on the board, it mattered little as the second-seed Russian cruised to take out the first set 6-1. Sharapova then led 5-1 and took out the second set to have little trouble with the 32-year-old American.
Sharapova now advances to the fourth round to face Belgian Kirsten Flipkens who earlier on Friday beat Russian Valeria Savinykh in three tight sets, 6-2, 4-6, 6-3.
The Russian four-time Grand Slam champion strode out onto Rod Laver Arena with a purpose, though, to begin the night session and now she has conceded just four games in three matches this Australian Open.
Sharapova's concession of just four games over the first three rounds equals German great Steffi Graf's 1989 mark as the fewest conceded by any woman to that stage of the Open since the move to 128-player draws in 1988.
She is on track for a quarter-final with Germany's Angelique Kerber, semi with China's Li Na or Poland's Agnieszka Radwanska, but with her form to date she deserves to be favourite to make the final from her half of the draw.
Sharapova said the meeting with Williams was something she had been eyeing since the draw was announced.
"No matter what she's ranked or seeded she's always a very tough opponent," Sharapova said.
"I was very determined out there and really wanted this victory."